एक्सरे और मणिभ संरचना

eksare aur manibh sanrachana dravy ki sanrachana ke adhyayan mean eksare ka vishesh sthan hai. dravy ke charam rachak paramanu haian. paramanuoan ka akar atyant sookshm hota hai, at: unake adhyayan ke lie atyant sookshm prakar ke sadhanoan ki avashyakata hoti hai. prakash ka tarangadairghy paramanuoan ke akar se bahut adhik hone ke karan sanrachanatmak adhyayan mean prakash ka vishesh upayog nahian ho sakata. eksare ka tarangadairdhy 1 aiangastram ke lagabhag evan paramanuoan ke akar se tulaniy hai, at: dravy ki sanrachana ke adhyayan ke lie eksare uchit sadhan hai. dravy ki gais, drav tatha thos in tinoan avasthaoan ke vishay mean eksare dvara atyant labhadayak jnan prapt hua hai. thos padartho ki (visheshat: manibhoan ki) sanrachana ka yatharth jnan sarvapratham eksare dvara hi hua. vartaman kal mean eksare-vishleshan ka pradhan uddeshy yah hai ki thos avastha mean paramanu kis prakar sthit tatha vitarit rahate haian, yah jnat kiya jae. ek ath va adhik tatvoan ke paramanu jab atyant nikat ate haian tab paramanuoan ke bahy ilektranoan mean parasparik kriya hoti hai. santulan hone ke pashchath‌ in paramanuoan ki aantim rachana mean sthitij oorja nyoonatam hoti hai. at: svatantr paramanu aur thos padarth ke baddh paramanu, in donoan ki oorjaoan mean bhed hota hai. svatantr paramanuoan se praranbh karake unaka thos padartho mean parivartan hone par oorja ka jo vinimay hota hai aur aant mean thos padartho ki jo sanrachanaean prapt hoti haian, unase thos padartho ke gunoan ki vyakhya karana saiddhaantik bhautiki ka ek uddeshy hai. vartaman kal mean anek gunoan (udaharanarth vidyuchchalakata, prakashakiy sthiraank, sphuradipti ityadi) ka spashtikaran karane mean adhikaansh saphalata mil chuki hai. yah spasht hai ki is prakar ke adhyayan ka keval bhautiki mean hi nahian, apitu rasayan, tekan aauloji ityadi vijnan ki any shakhaoan mean bhi atyant mahatv hai. thos padartho ke anek gun, unaki rasayanik kriyaean tatha svatantr paramanuoan ke gunoan ke parasparik sanbandh ka yatharth adhyayan karane ke lie thos padartho ki sanrachana ka jnan hona avashyak hai.

samanyat: sab thos padarth manibhamay hote haian; inamean apavad bahut tho de haian (udaharanarth kach, jise amanibh kaha ja sakata hai). anek thos padarth (udaharanarth dhatu) bahari roop mean manibh jaise nahian dikhaee dete haian, tathapi eksare-vishleshan se yah saralata se pramanit hota hai ki ye sab padarth bhi manibh haian. dhatu jaise padartho ke manibh atyant sookshm hote haian aur samanyat: unake kramabaddh sthapit n rahane se bahm roop mean dhatu manibh jaisi nahian dikhaee deti. uchit prakramoan se dhatuoan ke bhi isht akar ke manibh prapt ho sakate haian. parantu in dhatviy manibhoan ke aur unaki samany dhatuoan ke gun saman nahian rahate. at: thos padartho ke gun jin manibh sanrachanaoan par nirbhar hote haian, unake adhyayan ka mahatv spasht hi hai. eksare dvara manibhoan ki sanrachana ka adhyayan hone ke poorv manibhoan ke bahm gunoan ka bahut kuchh adhyayan ho chuka tha aur unake roopoan ke vishay mean svatantr manibh jyamiti sthapit ho chuki thi. eksare ki sahayata mean manibh sanrachana ka jo jnan prapt hua hai usaka uchit bodh hone ke lie is manibh jyamiti ka parichay avashyak hai.

manibh jyamiti tatha samamiti;-a. manibhoan ki visheshata unake bahy jyamitiy svaroop mean hai. manibh prishthoan se simit hote haian aur ye prishth jahaan milate haian vahaan korean tatha kone banate haian. in prishthoan ka ek doosare se samamit sanbandh hota hai. bahy svaroop ke parikshan se yah anuman nikala ja sakata hai ki manibhoan mean kuchh nishchit dishaean hoti haian aur unase bahy svaroop ka sanbandh rahata hai. is anuman ki siddhi manibhoan ke any gunoan se bhi hoti hai, jaise manibhoan ki vaidyut tatha ushmiy chalakata, kathorata, vartanaank ityadi gun manibh ke aksh ki disha par nirbhar rahate haian. manibh sanrachana ke adhyayan mean eksare ka upayog hone ke poorv hi yah anuman kiya gaya tha ki manibhoan ke uparyukt gunoan ka karan unake rachakoan ki kramabaddh sthapana par adhrit ho sakata hai. yadi uchit svaroop ke rachak lie jaean to tin ayamoan mean unaki punaravritti karake kisi bhi manibh ka svaroop prapt ho sakata hai. at: manibhoan ka svaroop jnat karane ke lie (1) pradhan akar (motif) aur (2) uchit vidhi se punaravritti karane ka sadhan, keval in do ki hi avashyakata hoti hai. pradhan akar ke spashtikaran ke lie pray: biandu lie jate haian aur tin ayamoan mean unaki punaravritti ke digjal (spes laitis) banaya jata hai. is digjal se manibh ki pratima (patarn) prapt hoti hai.

digjal ki kalpana se manibhoan ki sanrachana ka adhyayan kuchh sugam ho jata hai. chitr 1 mean ek digjal diya hai. isamean biandu kramanusar tin ayamoan (daimenshans) mean sthit haian aur unako kramanusar jo danevali rekhaoan se digjal banata hai, jo akriti mean moti rekhaoan se dikhaee gee hai. akriti mean yadyapi ek hi prakar ki ekak koshika dikhaee gee hai, tathapi vichar karane par yah spasht hoga ki aisi anek prakar ki kiantu saman ayatan ki ekak koshikaean is digjal mean banaee ja sakati haian. ekak koshika mean ath shirshabiandu haian, aur pratyek shirshabiandu aisi ath koshikaoan se sanbandhit hai. at: mana ja sakata hai ki pratyek koshika ke lie ek hi biandu hai. isaka arth yah hai ki pratyek koshika manibhapratima ki sanpoorn matrak hai. isi prakar se pratyek manibh ki samamiti ke anuroop uchit koshikaean nikali ja sakati haian. in ekak koshikaoan ki korean (ejez) laghutam lanbaiyoan ki hoti haian. 200px|left chitr 1-digjal tatha ekak koshika 200px|left chitr 2- ekak koshika aur usake avayav

ekak koshika ki tin koroan se tatha unake bich ke tin konoan se pratyek koshika nishchit hoti hai. koshikaoan ke in chhah avayavoan ko soochit karane ki atanrarashtriy paddhati hai, jisamean inake lie ABCOabg ka prayog hota hai. chitr 2 mean ek ekak koshika dikhaee gee hai. is chitr mean ABCOabg ke badale kramanusar ka kha ga moo a ee oo ka prayog kiya gaya hai. koshika ke avayav nimnalikhit haian :

lanbaee mooka = k; kon khamooga = a

lanbaee mookha = kh; kon gamooka = ee

lanbaee mooga = g; kon kamookha = oo

lanbaiyoan k,kh tatha g ko akshiy lanbaiyaan kahate haian aur mooka, mookha tatha mooga in tin dishtoan (vektars) se manibh ke akshoan ki paribhasha hoti hai. 'moo' ko mool biandu samajhakar manibh ke kisi bhi biandu ka sthan ikaiyoan k,kh, g mean nishchit ho sakata hai. udaharanat: yadi manibh ke kisi ek biandu ke nirdashaank y, r, l haian, to ham likh sakate haian ki

y=p×k

r=ph×kh }}jahaan p, ph, b dhan athava rrin sankhyaean athava shoony haian.

l=bag×

shh

digjal tatha ekak koshika ki kalpana se manibh ki anek vishishtataoan ka spashtikaran karana manibh jyamiti ka vikas karana saral hota hai. digjal ke bianduoan ki rachana samaantar tatha samadoorasth asankhy staroan dvara svechchhapoorvak ki ja sakati hai. ye star manibhoan ke pramukh phalakoan ke samaantar hote haian.

manibhoan ke phalak nirdharit karane ke lie pahale poorvokt staroan mean se tin asamaantar star lie jate haian. inako ham pradhan phalak kaheange. inake pratichchhedoan se mooka, mookha, mooga, tin manibh akshoan ki dishaean milati haian. ab ek any samatal aisa liya jata hai jo tinoan pradhan phalakoan ko katata hai; is samatal ko manak samatal (staiandard plen) kahate haian. yah yadi ka kha ga ho (chitr 2), to mooka, mookha aur mooga in aant:khandoan ki apekshik lanbaiyoan se manibh ki akshiy lanbaiyaan k, kh, g, nishchit ki jati haian. manibh ka bahy svaroop nishchit karane ke lie k, kh, g ki keval apekshik lanbaiyoan ki avashyakata hoti hai; at: samanyat: kh ki matra ek man li jati hai. k, kh, g ke nishchit ho jane par manibh ka koee bhi any tal manibh akshoan par usake aant: khandoan se nishchit hota hai. man lean ye aant:khand k/ch, kh/chh, g/j haian to ch, chh, j in sankhyaoan ko milar aank kahate haian. koee bhi phalak athava tal usake milar aankoan dvara, arthath‌ ch, chh, j dvara soochit kiya jata hai. chitr 2 mean tal ka kha ga (111) se soochit hoga. tal mookhaga ke samaantar kiantu biandu ka mean se janevala tal (100) se soochit hoga, karan yah hai ki is tal ke lie chh=j=µ.

jal ke kinhian bhi do bianduoan ko jo dane par jo saral rekha banati hai use badhane se bianduoan ki ek pankti milati hai, jisamean digjal ke samadoorasth biandu rahate haian. is pankti ko mandalaksh (zon aiksis) kahate haian. yadi jal ke kisi ek biandu ko, jisake nirdeshaank (tak, takh, dhag)haian, mool biandu se jo d diya jae to prapt pankti ki disha (t th dh) ek mandalaksh ki disha hoti hai. yadi is mandalaksh mean ghanepan se jal biandu ho to yah mandalaksh mahatv ke anek taloan ke samaantar hota hai.

anek manibhoan ke phalakoan ke kon napane se yah jnat hua ki manibhoan ke bahy svaroopoan mean jitani vibhinnata dikhaee deti hai utani vastav mean nahian hoti aur samast digjal keval sat samudayoan mean vibhajit kie ja sakate haian. any shabdoan mean, sab manibhoan ke mapit konoan ka tatha phalakoan ke milar aankoan ka sat nirdeshaank paddhatiyoan se spashtikaran ho sakata hai. at: manibhoan ke digjaloan ke keval sat prakar haian. chitr 2 mean ekak koshika ki akshiy lanbaiyaan tatha unake bich ke kon poorvokt sat paddhatiyoan mean bhinn bhinn haian. unaki napean nimnalikhit sarani 1 mean di huee hai :

sarani 1

sat manibh paddhatiyaan aur unake lakshan

shh

shh

digjal (chitr 2) ke bianduoan ke ath sthanoan ke atirikt any sthan bhi digjal biandu ke lie sanbhav hai. ye sthan ghan manibhoan ke lie chitr 3 mean die ge haian. saral ghan (chitr 3 (1)) mean ath konoan par ath biandu haian. inake atirikt ghan ke jo chhah phalak hote haian, unamean pratyek ke thik madhy par ek ek biandu sthapit karane se phalakakeandrit ghan (chitr 3 (2)) banata hai. saral ghan ke thik madhy par ek biandu sthapit karane se piandakeandrit ghan (chitr 3 (3)) banata hai. in vidhiyoan ke samavesh se tatha sarani 1 mean di huee sat paddhatiyoan se sarvajnat manibhoan ke digjal tatha keval 14 prakaroan mean vibhajit ho sakate haian (chitr 4 dekhie).

shh

chitr 3. ghan manibh

1. saral ghan; 2. phalakakeandrit (phres seantard) ghan;

3. piandakeandrit (b aaudi seantard) ghan.

a. yadi manibh thik vikasit hua ho to usaki bahy samamiti spashtata se dikhaee deti hai. adhyayan se is samamiti ke jo prakar spasht hue unako biandusamuday (pvaiant groop) kahate haian. biandusamuday ko thik se samajhane ke lie kuchh jyamitiy kriyaoan ka jnan avashyak hai. manibhoan ki samamiti mean nimnalikhit jyamitiy kriyaoan ke udaharan milate haian:

(1) kisi ek manibh aksh ke charoan or ek bar paribhraman karane mean (arthath‌ 360° ghoomane mean) yadi m sthitiyaan aisi hoan jo pratham sthiti se abhinn hoan to manibh ke us aksh ko m-bar paribhraman-samamiti-aksh kaha jata hai. any shabdoan mean, 'm-bar paribhraman-samamiti-aksh' ke parit: 2p/m aansh tak ghoomane se manibh poorvavath‌ sthiti mean a jata hai. udaharanarth, ghan manibh mean pratyek pramukh aksh 'chaturvar paribhraman samamiti-aksh' hota hai. prakriti mean is prakar ke keval dvi-var, tri-var, chaturvar tatha shadvar aksh hi hote haian, panch-var tatha any aksh nahian hote.

(2) yadi manibh mean ek aisa biandu a ho ki pratyek biandu b tatha usake sangat biandu b´ ko jo danevali saral rekha b a b´ biandu a par samadvibhajit hoti hai, to biandu a ko manibh ka samamiti keandr kaha jata hai. udaharanarth, ghan ka madhyabiandu samamiti keandr hota hai. samamiti keandr ko pratilomikaran keandr bhi kahate haian.

(3) yadi manibh keandr mean se hokar jata hua aisa tal mil sake ki manibh ka ek ardhabhag doosare ardhabhag ka (is tal mean) pratibianb ho, to aise tal ko samamiti tal kahate haian.

uparyukt varnit kriyaoan ki mishr kriyaean bhi ho sakati haian. yadi kisi keandriy aksh ke parit: 2p/m aansh tak paribhraman ke pashchath‌ pratilomikaran se pun: poorvavath‌ mool paristhiti prapt hoti ho, to is kriya ko paribhraman-pratilomikaran kahate haian. vaise hi 2p/m aansh tak paribhraman ke pashchath‌ paravartan se pun: poorvavath‌ rachana prapt hoti ho, to use paribhraman-paravartan kaha jata hai.

paravartan, paribhraman, pratilomikaran, paribhraman-pratilomikaran, paribhraman-paravartan ityadi pratyek kriya ko samamiti kriya kahate haian. inamean se ek athava adhik kriyaoan se manibhoan ke bahy svaroopoan ka spashtikaran ho sakata hai. kriyaoan ke in sab prakaroan ko biandusamuday kahate haian. sab manibhoan ke lie (arthath‌ sarani1mean di huee sat paddhatiyoan ke lie) keval 32 biandusamuday sanbhav haian. inako manibhavarg kahate haian.

k. manibhoan ke bahy svaroop tatha bhautik gunoan se unake biandusamudayoan ka nigaman ho sakata hai kiantu manibh ke charam rachak paramanu kis prakar sthit haian tatha usaki sanrachana mean kis prakar ki samamiti hai isaka yatharth jnan nahian ho sakata. paramanuoan ki sthiti ka jnan sarvapratham eksare se hua. ekak koshikaoan mean uparyukt prakaroan ki samamitiyaan hoti haian aur poorvokt kriyaoan se koshikaean pun: poorvavath‌ hoti haian. manibhoan mean in ekak koshikaoan ka vistar tin ayamoan mean hota hai. jin kriyaoan se pratyaksh manibh prapt hote haian, unhean diksamuday kahate haian. dikh‌ samudayoan ke 230 prakar haian.

diksamudayoan mean navin samamitiyoan ka astitv sanbhav hota hai, jo biandusamudayoan mean nahian ho sakata. visarpan taloan (glaid plens) ka spashtikaran chitr 5 se ho sakata hai. is akriti mean biandu k tatha kh kramanusar vritt tatha varg se soochit kie ge haian. dvitiy pankti ke biandu´ se tatha tritiy pankti ke biandu´´ se soochit kie ge haian. dvitiy tatha tritiy panktiyoan ke thik madhy par n n´ ek tal hai jo kagaj ke tal par abhilanb hai. is tal n n´ mean paravartan hone se dvitiy pankti ke biandu k tritiy pankti ke bianduoan kh ke sthanoan par chale jaeange. kiantu, yadi unako paravartan tal ke samaantar bianduoan (k athava kh) ki paraspar doori ke ardhabhag tak hataya jae, to paristhiti pun: poorvavath‌ ho jaegi. any shabdoan mean, n n´ tal mean paravartan ke pashchath‌ ardh-jal-doori ka sthanaantaran karane se panktiyoan pun: pratham sthiti se sanpati (koiansideant) ho jati, haian. is prakar ke tal ko (tal n n´ko) visarpan tal ho jati, haian. is prakar ke tal ko (glaid plen) kahate haian. tin ayamoan mean jal ko sanpati karane ke lie visarpan tal mean paravartan ke pashchath‌ pratham ardh-jal-doori ka sthanaantaran visarpan tal ke samaantar aur tath‌pashchath‌ visarpan tal se lanb disha mean ardh-jal-doori ka sthanaantaran karana avashyak hoga.

yadi n n´ ko ham aksh samajhean, to usake parit: 180° ke ghoornan se biandu k´ biandu kh´´ ke sthan par chala jayaga. ab ardh-jal-doori ka sthanaantaran karane se prapt akriti pratham akriti se sanpati hogi. in gunoan ke aksh ko (aksh n n´) peanch aksh (skroo aiksis) kahate haian. yadi bianduoan k (athava kh) ka ek doosare se aantar 'y' samajha jae to chitr 5 mean ka peanch aksh n n´ dvivar pech aksh hoga, kyoanki yahaan sanchalan y/2 ki avayakata hoti hai. trivar paianch aksh ke lie sthanaantaran y/3 ki tatha ghoornan 2p/3 ki avashyakata hogi athava m-barapeanch aksh ke lie sthanaantaran y/m tatha ghoornan 2p/m ki avashyakata hogi. 200px|left

chitr 4. digjal ke 14 prakar

1. traiklinik; 2. saral monoklinik; 3. aanty phalakakeandrit monoklinik; 4. saral aaurthor aaumbik; 5. aanty phalakakeandrit aaurthor aaumbik; 6. piandakeandrit aaurthor aaumbik; .phalakakeandrit aaurthor aaumbik; 8. heksagonal (shadbhujiy); 9. r aaumbohedrel; 10. saral tetragonal; 11. piandakeandrit tetragonal; 12. saral ghan; 13. piandakeandrit ghan; 14. phalakakeandrit ghan (akshiy lanbaiyaan tatha akshiy konoan ke lie sarani 1 dr.).

tin ayamoan mean jal siddhaant, jalabianduoan ke sthanoan par paramanuoan ki sthapana aur uparyukt visarpan tal tatha peanch aksh, inaka upayog karake shonaflij ne 19vian shatabdi ke aant mean manibhoan ke vargikaran mean sudhar kiya. jaloan ke 14 prakaroan ka (chitr 4) tatha 32 biandusamudayoan ka upayog karake 230 samuday pramanit kie ge haian. pratyek jnat manibh inamean ke ek dikh‌samuday ke anusar hota hai. eksare-vivartan (vyabhang) se manibhoan ke in jyamitiy siddhaantoan ka tatha dikh‌samudayoan ka pratyaksh praman milata hai. at: eksare-vishleshan mean dikh‌samuday jnat hona atyavashyak hota hai.

manibhoan ka eksare -vyabhang-lave, phhऱidarish aur knipiank ne prayog dvara pratham manibhoan ka eksare-vyabhang prasthapit kiya (dr. eksareoan ki prakriti). is vyabhang ka saiddhaantik spashtikaran lave ne kiya. manibhoan mean paramanu kramabaddh p mean sthit hote haian. jab kisi paramanu par eksare girate haian tab us paramanu dvara (vastut: us paramanu ke ilektranoan dvara) eksare ka prakirnan hota hai. yadi paramanuoan ki pankti li jae to unase prakirnan hone par tatha tarangikaoan ka sanyog hone par aant mean jo tarangagr prapt hoga, usaki disha mean vyabhang ke pashchath‌ eksare jaeange. kiantu sanyog hote samay path ka aantar shoony athava sanpoorn tarangadairghy (ek athavaadhik) ho sakata hai; at:, prakash ke vyabhang ke saman, shoony, pratham, dvitiy, tritiy ityadi kramoan ki eksare-vyabhanjit kiranean bhinn bhinn dishaoan mean mileangi. eksare ka tarangadairghy yadi dai samajha jae to jis disha mean kramik tarangikaoan dvara prakirit kiranoan ka m× dai pathaantar hoga, us disha mean prakirn kiran milegi. arthath‌ yah disha ek shankutal par hogi, kyoanki is shankutal ke shirsh se paridhi tak gee huee pratyek rekha ke lie uparyukt pratibandh santusht hoga. yah phal uchit parivartan karake do ayamoean mean paramanu-panktiyoan ke lie bhi anuprayojy hai. aur age badhakar yah phal uchit parivartanoan ke pashchath‌ tin ayamoan ki paramanu-panktiyoan ke lie (arthath‌ pratyaksh manibhoan ke lie) bhi anuprayojy hota hai. ganana se yah nishkarsh nikalata hai ki yadi jal ke paramanuoan se vyabhanjit hokar aksh moo ka (chitr 2 dr.) ki paramanu-pankti se kram p ka vyabhang hota ho, aur moo ga ki paramanu-pankti se kram m ka vyabhang hota ho to jyamiti ki drishti se tal p b m se paravartan ke tuly hai.

yahi phal braig ki riti se saralatapoorvak prapt hota hai. chitr 6 mean (1,1) manibh ke paramanoan ki ek pankti, tatha (2, 2) usake samip ki doosari pankti hai, arthath‌ (1,1) tatha (2,2) samaantar haian. tarangadairghy dai ka ekavarn eksare pratham pankti mean k par tatha dvitiy pankti mean kh par girata hai. paravirtanoan ke pashchath‌ kiran 2 mean pathaantar p kh ph hoga. yadi yah pathaantar n×t t ho, to eksare ka paravartan hoga. yah pratibandh nimnalikhit samikaran dvara vyakt ho sakata hai-

2 d jya tha = n × t...(1)

yahaan t = dai = tarangadairghy

samikaran (1) ko braig ka niyam kahate haian. samikaran (1) ke saral hone ke karan isaka adhik upayog kiya jata hai. yadyapi lave ki riti prakashiki ke jnat siddhaantoan ke anusar hai tathapi braig ki riti ki tulana mean vah adhik kathin hai. yadi eksare ka tarangaderghy dai jnat ho to samikaran (1) se vishisht talapaddhati ka aantaran (spesiang) d prapt karane ke lie keval kon th ka mapan karana p data hai. apati eksare ka tarangadairghy dai tatha jin manibh taloan se paravartan ho raha hai unake milar aank (ch, chh, j) se jal ka achar nikala ja sakata hai. ghan, tetra- 200px|left chitr 5. visarpan tal (glaid plen.)

gonal tatha aaurther aaumbik (jinake nirdeshaksh lanbakon hote haian) koshikaoan ke lie dach chh j ki matra nimnalikhat hoti hai :

d2ch chh j . . (2)

ghanakoshika mean k.= kh.= g.. ke anusar ghanakoshika ke lie

d2ch chh j

arthath‌ samikaran (1) ke anusar ghanakoshika ke lie

n × tajaya (than). . . . (3)

yahaan tham navean kram ka paravartan kon hai. isi prakar, ganana se pratyek prakar ki koshika ke ekak aksh doori ka mapan kiya ja sakata hai.

chitr 6. braig ka niyam; 2 d jya thu n t

yahaan d = manibh ki do samip ki paramanu panktiyoan ka aantar; t = apati ekavarn eksare ka tarangadairghy; th = paramanu-pankti tatha apati kiran ke bich ka kon (ise glaiansiang kon kahate haian); n = paravartan ka kramaank.

vyutkram jal (resiprokal laitis) -vivartan-pratima ke bianduoan ka vishleshan karate samay, jin manibh taloan se vivartan hota hai unaki pravanataoan (slops) ka mahatv spasht hota hai. pratima ka pratyek biandu vishisht samaantar taloan se braig ke niyamanusar paravartit hokar prapt hota hai. in taloan ki pravanata tal ke abhilanb (n aaurmal) se nishchit hoti hai. at: tal ke sthan par abhilanb ka upayog karane se ek labh yah hota hai ki tal ayamoan ke badale abhilanb ke do ayamoan ki hi avashyakata hoti hai, arthat ek ayam kam ho jata hai. eksare-vivartan pratima do ayamoan ke photo-philm par li jati hai aur yah pratima ek drishti se vibhinn pravanataoan ke tatha vibhinn prakirnan-kshamataoan ke manibhataloan ka saral kiya hua pradarshan hai. yadi ham uparyukt pratyek tal ke abhilanb ko is prakar nishchit karean ki is abhilanb ki disha pravanata nishchit kare tatha usaki lanbaee aantar-tal aantaran (spesiang) dach chh j se vyutkram ho, to in sab abhilanboan ke sire ke bianduoan se naya biandujal prapt hoga, jisaka eksare-vivartan-pratima se samy hoga. is navin biandujal ko vyutkram jal kahate haian. is prakar vyutpadit vyutkramajal atyant mahatv ka hota hai, kyoanki prayogoan se prapt eksare-vivartan-pratima is vyutkram-jal ka hi ek vikrit pratibianb hoti hai. saral samamiti ke (udaharanarth ghan paddhati ke) manibhoan se jo eksare-vivartan pratimaean prapt hoti haian, unaka vishleshan karake sanrachana nishchit karana vishesh kathin nahian hota, kiantu any manibhoan ke lie sanrachana ka nirnay karana atyant kathin hota hai aur yahaan vyutkram jal ka upayog atyavashyak hota hai. vyutkram-jal ka upayog tatha vistar visheshat: evald aur barnal ne kiya. vyutkram-jal ke upayog se manibh sanrachana ka nishchay karane mean vishesh suvidha huee aur samay tatha shram mean bahut bachat huee. vyutkramajal ke kuchh lakshan aur gun niche die hue haian. manibhoan mean dishaoan ka mahatv praranbh mean hi bataya gaya hai, at: manibh sanrachana ki ganana mean disht bijaganit (vektar ailajebra) ka upayog kiya jata hai. vyutkram jal ki ganana mean disht bigajanit ka hi upayog hota hai. samanyat: disht mote (thik) aksharoan mean tatha adisht sadharan aksharoan mean chhape jate haian.

disht jal ki ekak koshika k, kh, g, (A B C) in tin dishtoan se nishchit hoti hai, kyoanki yahaan pratyek disht se usaki lanbaee tatha disha bhi nishchit hoti hai. jal biandu ko mool biandu se jo danevala disht tr (y, r, l), [ R (x, y, z)] nimnalikhit dishtasamikaran ke anusar hota hai :

tr = y k + r kh + l g. . . . (4)

R= xA + yB + zC . . . (4)

yahaan y, r, l ki matraean dhan athava rrin poorn sankhya tatha shoony ho sakati haian. in dishtoan se vyutkram jal ki paribhasha ki jati hai. vyutkram jal tin mool disht k*, kh*, g* (A* B* C*) is prakar lie jate haian ki disht k*(A*) disht kh (B) tatha g (C) ke akshoan par, disht kh* (B*) disht k (A) tatha g (C) ke akshoan par aur disht g* (C*) disht k (A) tatha kh (B) akshoan par lanb hote haian. disht bijaganit ki bhasha mean yah phal nimnalikhit samikaran dvara bataya ja sakata hai:

k*.kh = k*.g = kh*.g = kh*.k = g*.k = g*.kh = 0. . . (5)

A*.B = A*.C = B*.C = B*.A = C*.A = C*.B = 0. . . (5)

yahaan do dishtoan ke bich ka biandu adisht gunanaphal ka chihn hai. vyutkramadishtoan ke pariman nimnalikhit samikaran se prapt hote haian:

k*.k = kh*.kh = g*.g = gh2 . . . (6)

A*.A = B*.B = C*.C = C2 . . . (6)

jahaan gh (C) ek achar hai. samanyat: gh ka man ek liya jata hai. vyutkram jal ki is paribhasha se usaki ekak koshika tatha any gun aur lakshan (udaharanarth vyutkram akshoan ki lanbaiyaan, kon, ayatan ityadi) vputpann kie ja sakate haian. vyutkram jal ka koee bhi disht tr (ch chh j) ho, to vah milar aankoan (ch chh j) ke tal par lanb hota hai. disht tr* (ch chh j) ka pariman tal (ch chh j) ke aantaran (spesiang) d ch chh j ka vyutkram hota hai. is sankshipt varnan se bhi yah spasht hoga ki vivartan pratima se manibh sanrachana ka adhyayan karane ke lie vyutkram jal upayukt sadhan hai. kisi bhi tal ke lie braig ke niyamanusar paravartan hone ke pratibandh prapt karane ke lie vyutkram jal se paravartan-gola tatha sima-gola nikale jate haian. inaki sahayata se vivartan pratima ka spashtakiran saralata se hota hai.

(1) prayogik ritiyaan-eksare dvara manibh sanrachana ka adhyayan karane ki pramukh ritiyaan niche di huee haian. inaka sankshipt varnan eksare ki prakriti mean milega.

(1) lave ki riti : is riti mean shvet eksare ka (jisamean anek tarangadairghy hote haian) upayog kiya jata hai. do soochi chhidroan mean se jane ke pashchath‌ eksare kiranean samaantar ho jati haian. tab unako manibh ke ek chhote se tuk de par p dane diya jata hai (chitr 7). manibh ki is prakar sthapana ki jati hai ki usaka pramukh aksh apati eksare ki disha se vishisht kon banata rahe–samanyat: yah kon 00 hota hai. apati eksare ke anek tarangadairghyo mean se uchit tarangadairghy ka braig ke niyam 2d jya th = n × t ke anusar paravartan hota hai. paravartit kiranean photo pattika par athava philm par abhilikhit hokar samanyat: samamit biandupratima banati haian. pratima ke biandu dirgh vrittakar vakroan par sthit rahate haian aur ye biandu a (arthath‌ manibh mean se sidhe janevale eksare se prapt biandu) mean se jate haian. keval saral samamiti ke manibhoan se samamit pratimaean milati haian, anyatha jatil pratimaean prapt hoti haian. kailasait manibh ki lave pratima namak ke manibh ki pratima jaisi saral aur samamit nahian hai (eksare ki prakriti shirshak lekh se sanlagn phalak dr., jisamean namak tatha kailasait manibh ki lave pratimaean di huee haian).

chitr 7. lave ki riti.

s. soochi chhidr; m. manibh; p. photo pattika

paravartan karanevale taloan mean se jinaka mandalaksh samany hota hai unase paravartit kiranean ek dirgh vritt par abhilikhit hoti haian. pratyek mandalaksh usake dirghavritt se jnat kiya ja sakata hai. pratyek biandu ke aank (arthath‌ jis tal se paravartan hokar yah biandu prapt hua hai, usake milar aank) jnat karane ke lie trivimalekhi (stiriograifik) athava shaankav (gn aaum aaunik) prakshepan ka upayog kiya jata hai.

lave ki riti ka mahatv adhikatar aitihasik hi hai. keval lave ki riti se manibh ki sanrachana ka yatharth jnan nahian ho sakata, parantu is riti se manibh ki sanrachana ka anuman kiya ja sakata hai. lave bianduoan ki samamiti se manibh ki samamiti ki kalpana ki ja sakati hai. sanrachana ka sanpoorn jnan hone ke lie any ritiyaan adhik upayukt hoti haian.

lave ki riti ke any upayog bhi ho sakate haian. manibh ko yadi bal se nat kiya jae athava yadi manibh banate samay usamean aantarik vikriti ho jae, to lave bianduoan mean bhi vikritiyaan ho jati haian. udaharanarth, samanyat: manibh ke jo lave biandu ate haian unaka dirghikaran ho jata hai. yadi dhatu ke patale tuk de ko eksare par karean to samanyat: lave bianduoan ke sthanoan par saman tivrata se sankeandr vritt prapt hote haian aur in vrittoan ka keandr sidhe janevale eksare ka biandu hota hai. dhatu mean yadi vikriti ho to keandriy biandu se ariy (trijiy) rekhaean milati haian. eksare pratimaoan ki in vikritiyoan se dhatu tatha manibh ki aantarik vikritiyoan ka adhyayan ho sakata hai. anek manibhoan mean (udaharanarth peantaerihthratol, sodiyam kloret, him ityadi mean) lahe bianduoan ke atirikt nistej, atikshn biandu bhi ate haian. manibh ka tap badhane se ye biandu kuchh adhik tikshn ho jate haian. sar si.vi.raman ke anuman ke anusar ye atikshn biandu (difyooz sp aaut) manibh ke vishisht kanpanoan se ate haian aur ye kanpan eksare ki kriya se utpann hote haian. kiantu l aaunsadel ke anuman ke anusar atikshn bianduoan ka astitv dib aauy-valar ke samikaran ka upayog karake pramanit ho sakata hai.

(2) choorn riti (paudar methad)–is riti ka upayog yoorop mean dib aauy tatha shiarar ne aur amarika mean hal ne kiya. yadi lave ki riti se manibh ke tuk de ke sthan par manibh ka mahin choorn rakha jae aur ekavarn eksare apati ho, to photo philm par sankeandr vritt abhilikhit hote haian. isaka karan saralata se samajha ja sakata hai; choorn mean manibh ke tal samast dishaoan mean phaile rahate haian aur unase paravartit kiranoean ka ek shankvakar kiranapuanj nikalata hai, jise photo philm dvara katane par vritt prapt hota hai. yadi vrittakar philm ka upayog kiya jae aur vritt ka keandr choorn ke sthan par ho, to paravartit kiranoan se varnakram ke saman rekhaean mileangi. is riti ka upayog karanee ke lie bhinn bhinn trijyaoan ke choorn-kaimare milate haian. trijya jitani adhik hoti hai utani hi vibhedan kshamata adhik hoti hai, kiantu prakashadarshan (eksapozar) ka samay bhi badhata jata hai. namak tatha kailasait ka choorn-varnakram (paudar spekta) eksare ki prakriti shirshak lekh se sanlagn phalak mean diya hua hai.

choorn mean manibh ke tal sab dishaoan mean bikhare hue rahate haian, at: choorn pratima mean in sab taloan se paravartan hokar varnakram milata hai. is riti mean varnakram ki rekhaoan ke milar aank jnat karana itana kathin nahian hota. braiga ke samikaran ka upayog karake pratyek rekha se dach chh j (dhkl) (jal-aantaran) ki matra prapt ho sakati hai. in matraoan se tatha varnakram-rekhaoan ke vitaran se choorn ke manibh ki sanrachana ka anuman kiya jata hai. udaharanarth, yadi ghanakar manibh lie jaean to unake tin prakar ho sakate haian (chitr 4 dr.). kiantu (ch chh j) ki matraean pratyek ke lie nimnalikhit bhaanti ki hoti haian :

dachachhaj

dhkl

is samikaran ka tatha sanrachana gunak (strakchar-faiktar)ka upayog karake yah phal milata hai ki (1) saral ghan mean ch, chh, j (nh, tth, thh) ki sab matraean sanbhav haian; (2) piandakeandrit ghan mean ch, chh, j, (nh, tth, thh) ka yogaphal sam hota hai; (3) phalakakeandrit ghan mean ch, chh, j (nh, tth, thh) ya to sab sam hote haian athava sab visham hote haian. yah phal chitr 8 mean dikhaya gaya hai. isaka upayog karake varnakram rekhaoan ke vitaran se manibh ki sanrachana ka anuman saralata se kiya ja sakata hai.

isi prakar ganana karake tetragonal, heksagonal, ityadi any manibhoan ke lie bhi saraniyaan banaee gee haian. inaka upayog karake pratimaoan se manibhoan ki sanrachanaoan ka anuman kiya ja sakata hai, kiantu any manibhoan ke lie kary itana saral nahian hai.

chitr 8. ghan manibh ke vibhinn prakaroan ke choorn-varnakram rekhaoan ka paraspar sanbandh

(k) saral ghan, (kh) piandakeandrit ghan, (g) phalakeandrit ghan. saral ghan mean sabase adhik, piandakeandrit ghan mean usase kam tatha phalakakeandrit ghan mean sabase kam rekhaean hoti haian.

is praddhati ke any anek upayog hote haian. pratyek shuddh manibh ki vishisht choorn-varnakram-rekhaean hoti haian aur unase vah manibh pahachana ja sakata hai (jaise paramanviy varnakramoan se tatv pahachane jate haian). at: ajnat mishran tatha padarth ka rasayanik vishleshan karana choorn riti se atyant saral hota hai. isake lie henavalt, rin tatha phrehvel ne anek padartho ke lie saraniyaan banaee haian. choorn varnakram ki rekhaoan ki sthiti ka tatha unaki tivrata ka mapan karake in saraniyoan se padarth athava mishranoan ka rasayanik vishleshan shighratapoorvak kiya jata hai. yadi padarth atyant svalp matra mean ho to bhi choorn-riti se usaka sookshm vishleshan (gaigar-daphraiiktomitar) ke upayog se choorn riti sulabh ho gee hai. isake pahale choorn riti mean jo varnakram photo philm par milata tha usake lie 6 se lekar 12 ghante tak lagate the. isake pashchath‌ photo philm ko develap karane, sukhane ityadi mean bhi 2-3 ghantoan ki avashyakata hoti thi. tatpashchath‌ varnakram rekhaoan ka mapan aur aant mean pratyek rekha ki tivrata ka sookshm dipti-mapi (maikrophotomitar) se mapan ityadi karyo mean bahut samay lagata hai. kiantu gaigar vyabhangamapi se ye sab kriyaean ek sath shighratapoorvak hoti haian. 200px|left chitr 9. ghoornit-manibh riti

k. eksare samaantaritr (k aaulimetar); kh manibh; g. photo philm; gh. laghukarak yoktr (ridakshan giar); n motar.

(3) ghoornit-manibh riti–is riti ka upayog pahale pahal sibold aur polanyi ne kiya. yah sabase adhik upayukt riti hai, at: ajakal isi riti par ashrit kee sudhari huee ritiyaan prachalit haian. inamean se uchit riti chunakar samany: kisi bhi manibh ki sanrachana ka vishleshan kiya ja sakata hai.

chitr 9 mean samany ghoornit-manibh dikhaee gee hai. ekavarg eks kirarn samaantaritr k mean se par hokar samaantar hoti haian aur manibh kh ek dhuri (shaipht) par sthit rahata hai aur ek vidyutt motar tatha laghukarak yoktr (ridakshan giar) ki sahayata se is dhuri ko mand veg se ghumaya jata hai. photo philm ya to chapati rahati hai athava belanakar philm prayukt hota hai; isase paravartan kon ka paras bahut badh jata hai tatha vishleshan ke lie pratima adhik saral ho jati hai. manibh konamapi ke shikhar par manibh rakha jata hai aur usaka ek pramukh aksh ghoornan par rakha jata hai.

is paristhiti mean ek pratima lene ke pashchath‌ manibh ko 90roo kon dvara ghuma diya jata hai aur doosari pratima li jati hai. manibh ko pun 90roo kon dvara ghuma diya jata hai, kiantu is samay ghumane ka aksh ghoornan aksh ke lanbavath‌ hota hai; ab pun pratima li jati hai. is prakar tin paraspar lanbakon akshoan ki dishaoan mean tin pratimaean li jati haian aur unase manibh ke sanbandh mean avashyak jnan prapt kiya jata hai. eksare ki prakriti shirshak lekh se sanlagn phalak mean abhrak ki ek ghoornit pratima di gee hai.

kabhi kabhi sanpoorn paribhraman ke badale manibh ki sanrachana ke anusar use vishisht konoan dvara ghumakar pratima li jati hai. yah pratima sanpoorn paribhraman se li huee pratima se saral hoti hai. avashyak hone par dolan ka kon kramash: badhakar anek pratimaean li jati haian. aisi pratimaoan se vishleshan karana saral hota hai.

yadyapi ghoornit manibh riti atyant upayukt hoti hai tathapi pratimaoan ke vishleshan mean anek sanshay rah jate haian. unako door karane ke lie anek prakar ke ne kaimaroan ka nirman kiya gaya hai. inamean vaijanabarg kaimara vishesh prasiddh hai. vaijanabarg kaimara ke pramukh aang, unaka sanbandh tatha kary chitr 10 mean dikhae ge haian.

vaijanabarg kaimara mean ekavarn eksare manibh par poorvavath‌ apati hote haian aur manibh ka ghoornanaksh usake ek mukhy aksh ke samaantar hota hai. philm belanakar hota hai aur is belan ka aksh ghoornanaksh se sanpati (koiansideant) hota hai. is kaimare mean philm sthir nahian rahata. usaka mand gati se sthanaantaran hota rahata hai aur yah sthanaantaran manibh ke ghoornan se samakramik hota hai. philm ke sthanaantaran ki yojana se vaijanabarg kaimare ki vishishtata spasht hogi. samany ghoornit-manibh riti mean philm sthir (steshanari) rahata hai, isalie manibh ke jin taloan ke jalaantaran saman rahate haian unake lie paravartan kon saman rahata hai. at: pratima ka ek biandu prapt hota hai aur jab ek doosara saman jal-aantaran ka tal paravartan ke lie uchit paristhiti par pahuanchata hai tab tak philm ka sthanaantaran ho jata hai aur saman jal-aantaranoan ke bhinn bhinn taloan se prithakh‌ biandu milate haian. 200px|left chitr 10. vaijanabarg kaimare ki sanrachana

m. manibh; b. belanakar philm; gh. manibh ke ghoornan ki yojana; vi u philm ke ('gh' se samakramik) visthapan ki yojana.

vejanabarg kaimare ki saphalata ke pashchath‌ usamean sudhar karake anek kaimare vishesh uddeshyoan ke lie banae ge. inamean sibolt-sautar, bargar ityadi vaijnanikoan ke kaimare ullekhaniy haian.

ghoornit-manibh pratima se manibh sanrachana jnat karana adhik saral hota hai. visheshat: jin manibhoan ki sanrachanaean saral samamit nahian haian unake lie ghoornit-manibh riti athava is riti par adharit any kaimaroan ka upayog atyavashyak hai. chitr 9 mean di huee prayogik rachana ke anusar jo pratimaean ati haian unaka spashtikaran nimnalikhit prakar se ho sakata hai:

(1) rashmiyoan ki dishaean hjhr chitr 11 (1)

kisi mahatvapoorn mandalaksh ke ghoornanaksh ke samaantar rahane par eksare pratima mean jo stararekhaean (lear laians) ati haian unaka astitv chitr 11 se spasht ho sakata hai. jab apati samaantar tatha ekavarn rekhaoan ka vyabhang paramanuoan k tatha kh se hota hai, hjhrachitr 11 (1) t tab ve kiranean jinaka pathaantar ek sanpoorn tarangadairghy hota hai disha kh khavh mean jati haian. jinaka pathaantar (kh khavvh) do tarangadairghyoan ka hota hai, ve disha kh khavvh mean jati haian. ghoornan hote samay aise anek tal kramash: is sthiti mean aeange aur braig ke niyamanusar unaka pararvatan hoga. at: jin kiranoan ka pathaantar kh gavvh hai, ve doosare shanku par hoangi (chitr 11-2) aur jinaka pathaantar kh gavvhai, to philm phailane par ye sab biandu ek rekha par raheange aur yadi philm chapati ho (chitr 11-3) to pratyek shanku se prapt biandu ek atiparavalay (haiparabola) par raheange. yadi ghoornan aksh se manibh ka g-aksh samaantar ho to us aksh se samaantar sabhi taloan se kshaitij paravartan hoga aur biandu madhyavarti saral rekha par prapt hoange. arthath‌ is madhyavarti rekha par sthit bianduoan ke milar aank (ch, chh, 0), (nh tth thh) hoange . is madhyavarti saral rekha ko 'shoony star' rekha kahate haian. isi prakar star rekha ke oopar jo biandu hote haian unake milar aank (ch, chh, 0), (nh tth thh) hoange. yadi eksare ki disha tatha pratham star rekha ke bich ka kon ph () ho to usake mapan se g (kh) ki matra nikali ja sakati hai, karan

g jya ph u dai (kh chtd  ujhhn)

jahaan dai (hkhr) apati ekavarg eksavarn ka tarangadairghy hai. vyutkram jal ka upayog karane par in pratimaoan ka vishleshan adhik saral ho jata hai. vaijanabarg kaimare se jo pratimaean ati haian unaka roop bhinn hota hai, kiantu unase nirnay karana adhik sugam hota hai.

shh

(2)belanakar philm (3) chapati philm

hjhr chitr 11 (2, 3) t–ghoornit-manim eksare pratima ki stararekhaoan ka spashtikaran

(4) uparyukt ritiyoan se manibh ki samamiti nishchit hoti hai, kiantu usaki sanrachana nishchit karane ke lie adhik kary ki avashyakata hoti hai. yadi keval pratima ke bianduoan ki samamiti se manibh sanrachana ka anuman kiya jae, to ek se adhik prakar ki sanrachana sanbhav hai, aur inamean se uchit sanrachana ka nirnay karana kathin hota hai. yah samasya hal karane ke lie pratima ke bianduoan ki (athava rekhaoan ki) tivrata ka mapan avashyak hai aur is mapan ke pashchath‌ hi sanrachana nishchit ki ja sakati hai. yadyapi do bhinn prakar ke dikh‌samuday ek hi prakar ki samamit pratima de sakate haian, tathapi unaki tivrataean bhinn hogi. at: kis prakar ki sanrachana se pratima mean kis prakar tivrataoan ka vitaran hoga, yah jnat hona avashyak hai.

pratishthit (klaisikal) bhautiki ke anusar eksare tarangoan ka prakirnan ilektranoan se hota hai. pratyek paramanu mean ilektran hote haian aur pratyek ilektran se prakirnan hone par eksare ka aant mean sanpoorn paramanu se prakirnan hoga. at: vishisht dishaoan mean eksareoan ki tivrata in ilektranoan ke vitaran par avalanbit hogi. sanpoorn paramanu se prakirnan hone par tanrag ka vishisht disha mean ayam aur usi tarang ke ek mukt ilektran se unhian pratibandhoan ke aantargat pratishthit bhautiki ke anusar prapt ayam, in donoan ke anupat ko paramanviy sanrachana-gunakhand ganana dvara prapt kiya gaya hai. pratyek ekak-koshika mean samanyat: ek se adhik sankhya ke tatha prakar ke paramanu hote haian. in sab paramanuoan ko samavisht karake vishisht disha mean tarang ka jo ayam hota hai usako manibh ka sanrachana ayam kahate haian. is sanrachana-ayam se paramanuoan ke nirdeshaankoan ka sanbandh rahata hai. bhinn bhinn taloan ke lie ganana karake manibh-sanrachana-gunanakhand prapt kie ge haian.

eksare dvara manibh sanrachana ke nirnay ka marg ab spasht ho gaya hoga. eksare vyabhang pratima ke bianduoan ki (athava rekhaoan ki) tivrataoan ka mapan karake bhinn bhinn taloan ke manibh-sanrachana-gunanakhand prayog dvara pahale prapt kar lie jate haian. inase manibh ke paramanuoan ke sthanoan ka sannikatata se anuman kiya ja sakata hai aur unake nirdeshaankoan ka upayog karake pramanit samikaranoan se manibh-sanrachana-gunanakhand ki ganana ki jati hai. yadi anuman thik ho, to is ganana ke phal mean aur prayogik matra mean vishesh bhed nahian hota. isake pashchath‌ phoorievishelashan se ekak koshika mean ilektranoan ki ghanata nikali jati haian. is vishleshan phal se yadi aisa pramanit ho ki anumanit sanrachana paryapt uchit nahian thi, to is vishleshan phal dvara prapt sanrachana se pun: vishleshan kiya jata hai. is prakar anek bar kramik sannikatata se vishleshan karake aant mean yatharth manibh sanrachana prapt hoti hai. is vyutpodit manibh sanrachana se manibh ke any gunoan ka (udaharanarth prakashiy, chuanbakiy, vidyutiy ityadi gunoan ka) bhi spashtikaran hona avashyak hota hai, anyatha anumanit tatha vyutpadit manibh sanrachana thik nahian mani ja sakati .

(6) upasanhar –uparyukt ritiyoan se eksare vyabhang ke vishleshan ke pashchath‌ anek thos padartho ki sanrachanaoan ka nirnay hua hai. anek granth haian jinamean is prakar prapt thos padartho ki sanrachanaean di gee haian. pratyek tatv, unake yaugik padarth tatha karbadhatvik yaugik padarth ityadi thos padartho ki sanrachanaean bhi in granthoan mean mileangi.

manibh sanrachana ke jyamitiy sanbandh saral yaugikoan mean spashtata se dikhaee p date haian. aise padartho mean paramanuoan ke ayan hote haian, at: inako ayaniy manibh kaha jata hai. udaharanarth, namak mean sodiyam paramanu ka bahy ilektran door rahata hai. aur isalie sodiyam paramanu dhan aveshit ayan hota hai. sodiyam paramanu ka ilektran klorin paramanu se sanyukt ho jane par rrin aveshit ayan ho jata hai. dhan aur rrin ayan akarshit hokar pas aeange kiantu paramanu ke any ilektranoan ke tivr pratikarshan ke karan ek vishesh sima tak hi ye paramanu a paeange aur vahaan ve santulit ho jaeange. pratyek ayan viruddh avesh ke ayan se pariveshtit rahata hai. namak mean pratyek sodiyam ayan 6 klorin ayanoan se pariveshtit rahata hai. kiantu kshariy khanij ke kloraid, brimaid tatha ayodaid mean pratyek ayan viruddh avesh ke 8 ayanoan se pariveshtit rahata hai. yadi dhan aur rrin ayanoan ki trijyaoan ka anupat kam ho (0.51), to b da 4 chhote ayanoan se pariveshtit hota hai, udaharanarth ziank bleand athava voortasait.

dhatuoan ki sanrachana anek drishti se mahatvapoorn hai. samanyat dhatuoan ki sanrachana tin prakar ki hoti hai : (1) phalakakeandrit ghan, (2) piandakeandrit ghan aur (3) shadbhujiy saghan samooh (heksagonal klozapaikh‌d). eksare se dhatu ki keval sanrachana hi nahian apitu any gunoan ka bhi spashtikaran hota hai; udaharanarth, unake kanoan ka akar tatha vitaran, aantarik vikriti, ityadi. dhatuoan ke tar khianchate samay unake manibh vishesh dishaoan mean sthapit ho jate haian aur aisi paristhiti mean eksare vyabhang se jo pratimaean ati haian unako tantupratima (faibar paitarn) kaha jata hai. in pratimaoan mean vrittoan ki paridhi saman tivrata ki nahian hoti haian.

panne ki pragati avastha

adhar

prarambhik

madhyamik

poornata

shodh

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