thos avastha bhautiki

heera ki sanrachana ka chalit drushya

thos avastha ki bhautiki (Solid-state physics) ko thos avastha ka siddhaant (Solid-state theory) ke naam se bhi jaana jaata hai. yeh bhautiki ki vah shaakha hai jismein thos ki sanrachana aur uske bhautik gunon ka adhyayan kiya jaata hai. yeh sanghanit praavastha bhautiki ki sabse badi shaakha hai. thos avastha bhautiki mein is baat par vichaar kiya jaata hai ki thoson ke vaahya gun unke parmaanu-stareeya gunon se kis prakaar sambandhit hain. is prakaar thos avastha bhautiki, padaarth vigyaan ka saiddhaantik aadhaar banaati hai. iske alaava traanjistaron ki praudyogiki evam ardhachaalakon ki takaneeki aadi mein iska seedha upayog bhi hota hai.

anukram

pramukh upavibhaag

is vishay ke pramukh vibhaag hain :

1. sanrachana par aadhaarit gun, jaise manibh vigyaan, dhaatuon ki sanrachana ka siddhaant, mishradhaatueain, aayanik manibh, sansanjak (cohesive) bal, pattit sanrachana (band structure) aadi ;

2. pradhaanat: samaang (homogeneous) thoson ke gun, jaise vishisht ooshma, ooshmeeya kanpan, ooshmeeya tatha vaidyuchchaalakata, atichaalakata, prakaash sanvaahakata (photo conductivity), chunbakeeya tatha vidyutpaarak (dielectric) aadi

3. thos mein vishmaangata tatha vikrutijnya gun, jaise apadravyata, ardhachaalakata, plaistikta, jaalak (lattice) sanrachana dosh, rang kendra bindu dosh, visthaapan siddhaant, manibhvikaas aadi.

thos dasha ke baare mein jyon-jyon hamaari jaankaari badh rahi hai tyon-tyon antim ullikhit gunon par dhyaan adhik maatra mein aakrusht hota ja raha hai.

parichay

paramaanavik vinimay

dravya teen vibhinn avasthaaon mein paaya jaata hai - thos, drav tatha gas. gas avastha mein ghanatv atyant kam hota hai tatha sanpeedan saamarthya atyadhik. iske vipreet thos tatha drav ka ghanatv apekshaakrut adhik hota hai, kintu sanpeedan atyant kam. saadhaaran daab evam taap par gas ke ikaai aayatan ki sanhati samaan aayatanavaale thos ya drav ki sanhati ka lagbhag sahasraansh hoti hai. apni adhik sanpeedan saamarthya ke kaaran hi gaisein jis baratan mein rakhi jaati hain use ve poornataya bhar deti hain. thos ka aayatan daab ke ghataane badhaane se bahut kam badalta hai aur iska aakaar bhi nishchit hota hai. thoson mein kartanavikaar (shear strain) ho sakta hai, jab ki gas ya drav mein yeh gun upasthit naheen hota.

thos aur gaison ke bhautik gunon ke antar ke aadhaar par samajhaaya ja sakta hai ki gas ke paramaanuon ke beech ki doori thos ya drav ke paramaanuon ki beech ki doori ki apeksha yathesht adhik hoti hai. chooainki gas ke ikaai aayatan mein paramaanuon ki sankhya apekshaakrut kam hoti hai, at: usaka ghanatv bhi thoda hi hota hai. fir paramaanuon ke beech adhik doori hone ke kaaran ant:paramaanaveeya bal bhi ksheen hote hain. at: inmein ant:paramaanaveeya dooriyon ko saralata se badla ja sakta hai. gaiseeya avastha ki vyaakhya mein ant:paramaanaveeya balon ko ekdam naganya maana ja sakta hai, kintu thos aur drav ke siddhaanton ke viksan mein aisa naheen kiya ja sakta. is dasha mein ant:paramaanaveeya balon ka spasht roop se vichaar karna hoga, kyonki inmein parmaanu ek doosare ke nikat hain aur inke beech laganevaale bal shaktishaali hain. ant:paramaanaveeya bal kai prakaar ke hote hain, at: thos ke gunon mein gas ki apeksha adhik bhinnata pai jaati hai. udaaharan ke liye, paara tatha aargan gaiseeya avastha mein bahut samaan gun pradarshit karte hain, jabki thos aur drav dasha mein inke gunon mein yathesht antar paaya jaata hai.

thos do shreniyon mein vibhaajit kiye gaye hain, manibheeya tatha amanibheeya. manibheeya thoson (jaise dhaatuon tatha khanij padaarthon) ke andar paramaanuon ki vyavastha mein ooainche darje ki kramabaddhata pai jaati hai. amanibheeya thos (jaise kaanch ya plastic) mein anu tatha parmaanu kisi nishchit kram se vyavasthit naheen hote. manibheeya thos paaainch spasht shaakhaaon mein vibhaajit kiye gaye hain :

1. dhaatu aur mishradhaatu,

2. lavan (aayanik manibh),

3. sanyoji (valence) manibh,

4. anu manibh tatha

5. ardhachaalak.

dhaatu aur mishradhaatuon mein vidyuchchaalakata tatha dhaatvik chamak pai jaati hai. inmein vidyuchchaalakata ka gun mukt ilektraanon ke idhar-udhar vichran ke kaaran utpann hota hai. lavan mein aaveshit aayan hote hain. sanyoji manibh kathor padaarth hote hain, jaise heera aur silikn kaarbaaid. inka galanaank ooaincha hota hai tatha inka nirmaan praarambhik sanyoji rasaayanashaastr ke niyamon ke anusaar hota hai. anu manibh (jaise shushk him) aise thos hain jinke andar sthaayi anuon ko baaaindh rakhanevaale bal atyant alp hote hain. arthachaalak, jaise jink oksaaid ya kaupar oksaaid, aise thos hote hain, jinmein vichran karanevaale ilektraanon dvaara utpann honevaali vidyuchchaalakata ksheen maatra mein hi pai jaati hai.

amanibh thos (jaise akaarbanik padaarth) unheen gunon ka pradarshan karte hain, jo aanavik tatha sanyoji manibhon mein paae jaate hain. inki rachana bade aakaar ke anuon dvaara hoti hai, jinke beech ke badhanabal ksheen hote hain tatha sanyoji bandhan prabal.

thos avastha ke adhyayan ke liye keval manibh thoson par hi, jinke andar ke parmaanu trivimiteeya jaaleenuma (laitis) dhaaainche ke anusaar teen svatantr dishaaon mein vyavasthit hote hain, vichaar kiya jaata hai. is adhyayan mein kaaainch ya bahulak (polymer) ke gun bhi sanmilit kiye ja sakte hain, yadyapi inke andar manibhon ki tulana mein sanrachanaatmak niymitta nimnatar koti ki hoti hai. kaaainch ki sanrachana trivimiteeya jaali sadrush hoti hai. yeh aavarti naheen hoti. bahulak ka nirmaan bade aakaar ke anuon ke samaantar samoohon se hota hai, jinki sanrachana kuchh avasthaaon mein manibhon ke sadrush bhi ho sakti hai.

saamaanyat: pratibl padne par thos drudhta ka gun pradarshit karte hain. sangat vikruti (strain) bahut kuchh prativrti hoti hai. fir bhi sthir bhaar daalne par kuchh na kuchh shyaaneeya pravaah utpann ho hi jaata hai.

aitihaasik vikaas

thos avastha ke siddhaant ke adhyayan ke vikaas ko chaar charanon mein vibhkt kiya ja sakta hai :

1. sthool (macroscopic) gun, visheshataya sthool samamiti ;

2. jaaleeya (lattice) siddhaant tatha jaaleeya model ;

3. paripoorn manibhon ke gunon ka parmaanu siddhaant dvaara pratipaadan tatha

4. manibhon ki apoornata ke siddhaant ka vikaas.

punarjaagaran (Renaissance) kaal se lekar, jabki is vishay ke adhyayan ka praarambh hua tha, pichhli shataabdi ke ant tak logon ka dhyaan pratham charan par vishesh roop se keindrit raha tha. jaaleeya siddhaant mein ruchi aarambh mein keval amoort ya saiddhaantik pahaloo tak hi seemit rahi. isne vyaavahaarik roop tab dhaaran kiya, jab pratham mahaayuddh ke theek poorv is baat ki khoj ki ja chuki thi ki manibhon ki jaaleeya sanrachana se ex kirnon ka vivrtan ek adviteeya dhang se hota hai. manibhon ke gunon ke praathamik nirdhaaran ke liye parmaanu siddhaant pichhli shataabdi ke ant mein pehli baar laagoo kiya gaya. par is paddhati ne san 1925 aur 1928 ke beech, jab aadhunik kvaantam yaantriki evam tarang yaantriki ka samuchit vikaas ho chuka tha, poornata praapt ki. manibhon ki apoornata ka vyavasthit adhyayan san 1925 ke lagbhag aarambh hua. yeh apne charam vikaas par san 1945 ke baad pahuaincha.

adhyayan kshetr

thos avastha ke siddhaant ka lakshya thos ke vibhinn gunon ka paaramaanavik tatha naabhikeeya siddhaanton ke aadhaar par pratipaadan karna hai. ab tak vistaar se adhyayan kiye gaye vishay nimnalikhit hain : pratyaasthi tatha sughatya aacharan, sansanjan tatha sansanjan oorjaaeain, ilektrauvaneeya parivhan (vaidyut tatha ooshmeeya chaalakata, haal prabhaav, taapavidyut); aayaneeya parivhan (vidyutparivhan, raasaayanik aur rediydharmi visran); vishisht ooshma; chunbakeeya gun; vidyutpaarak gun; fero vaidyut gun; prakaasheeya gun (jismein prakaash sanvaahakata tatha sandeepti sanmilit hain) tatha naabhikeeya aur ilektrauneeya anuvaad.

thos avastha ke siddhaant ke antargat kiye jaanevaale maulik vaigyaanik anusandhaanon ki paridhi mein uparyukt kshetr aate hain. in kshetron ke katipya bruhat ansh vyaavahaarik ya takaneeki kaaranon se vishesh mahatva praapt kar sake hain. takaneeki kshetron ka vibhaajan pradhaanat: is prakaar hai : dhaatukarm ; ardhachaalak (jismein traijistar taiknaulauji bhi sanmilit hai) ; mruttika shilp (ceramics), jo lavan tatha sanyoji manibhon ke gunon par aadhaarit hai ; bahulak rasaayan (polymer chemistry) tatha chunbakeeyata. thoseeya avastha ke mesaron (masers) ke vishay ne, jo ek vishesh prakaar ke ilektrauneeya anunaad ko pradarshit karanevaale padaarthon se sambandhit hai, aadhunik teknauloji mein pramukh sthaan praapt kar liya hai.

thos ki paramaanuk sanrachana

vibhinn thoson ke gunon ki vibhinnata unke sanghatak paramaanuon ke beechavaale balon ke antar tatha paramaanuon ki kramavyavastha ki vibhinnata ke kaaran hai. parmaanu siddhaant ke anusaar parmaanu jab door-door rahate hain to ve ek doosare ko aakarshit karte hain aur jab ve ek doosare ke atyant nikat rahate hain to ve ek doosare ko pratikrshit karte hain. vibhinn paramaanuon ke beech pratikriya ki oorja pehle to ghatati hai, fir nyoonatam maan dhaaran kar leti hai aur tab yeh hathaat badh jaati hai. nyoonatam maan us vakt hota hai jab aakarshan aur pratikrshan ke bal ek doosare ke baraabar ho jaate hain. nyoonatam oorja ke liye paramaanuon ki sthiti is baat par nirbhar karti hai ki ye parmaanu kis raasaayanik shreni ke hain. nyoonatam paraspar kriya ke parimaan se ant:paramaanaveeya bandhan ki prabalata ki naap gyaat hoti hai. thos ke bheetar paramaanuvitran ki vyavastha ka pata ex-kirnon ki madad se lagaate hain. manibh thoson par kiye gaye prayogon ke anusaar trivimiteeya jaaleeya sanrachana ke pratyek falak par paramaanuon ka samaan vitran hota hai. amanibheeya thos ke andar paramaanuon ki vyavastha mein niyamit kramabaddhata nimnatar koti ki pai jaati hai.

thos ki raasaayanik sanrachana

ksheen vidyuchchaalakataavaale thos, jaise saamaanya dhaatuon ke oksaaid tatha kloraaid, pairaafin, tatha visanvaahi amanibheeya thos, jaise silika kaaainch, rasaayan ke saamaanya sanyojakata siddhaant ke niyamon ka paalan karte hain.

iske pratikool ooainchi vidyuchchaalakataavaali dhaatueain ek doosare ke saath sanyojakata rasaayan ke saamaanya niyamon ke anusaar sanyog karti hain. udaaharan ke liye taaainba bina apni jaaleeya sanrachana mein antar utpann kiye hue 30 pratishat tak jasta apne mein vilay kar sakta hai. ye dhaatueain yaugikon ka nirmaan karti hain jo sanyog karanevaale avayavon ke gunon se koi saadrushya naheen rakhate. udaaharan ke liye, taaainba aur jasta se ve yaugik bante hain jinke sootr taaya (CuZn) tatha taa5 ya8 (Cu5 Zn8) hain. dhaatvik sanyojan ke yaugik do prakaar ke ho sakte hain : pratisthaapit (substitutional) mishradhaatu tatha antaraaleeya (interstitial) mishradhaatu. inke sanyojan ke niyamon ka adhyayan hyoom rothare (Hume-Rothery) tatha haig (Hagg) ne kiya. pratisthaapit mishradhaatu mein vilyanaseema ke andar sanghatak dhaatuon ka anupaat jyon-jyon badalta hai tyon-tyon ek dhaatu ke parmaanu doosare dhaatu ke paramaanuon dvaara pratisthaapit hote jaate hain. yeh paaya gaya hai ki in yaugikon mein donon dhaatuon ke paramaanuon ke vyaas mein 15 pratishat se adhik ka antar naheen hota. iska udaaharan hai taaainbe mein jaste ko vibhinn anupaat mein milaakar praapt ki jaanevaali peetal ki alag-alag kismein.

antaraaleeya mishradhaatuon mein ek dhaatu ke parmaanu itne chhote hote hain ki ve doosari dhaatu ke parmaanu ki jagah par fit baith sakein. at: in dhaatuon ke jaaleeya dhaaainche ka kuchh bhaag doosari dhaatu ke parmaanu dvaara nirmit rahata hai. sanyog karanevaali dhaatueain yadi vidyudvaahak shreni mein ek doosare ke nikat sthit hon aur yadi chhote aakaaravaale parmaanu ka vyaas doosari dhaatu ke parmaanu ke vyaas ke 0.59 gune se kam ho, tab ye sahaj hi antaraaleeya mishradhaatueain bana leti hain. lohe mein kaarban ke vilay hone se bananevaali mishradhaatueain is jaati ka udaaharan hain.

thos ki bhautik aakruti nirdhaarit karanevaale siddhaant ooshma gativijnyaaan mein kisi nikaaya ki sthaayi avastha ko vyaavahaarik kaaryon ke liye niroopit karne ke liye aavashyak hai ki (F=E-TS) nyoonatam hon. yahaaain (F) mukt oorja hai, (E) us nikaaya ki oorja hai, (T) taap hai aur (S) entropi hai. paramashoonya taap par (F=E). at: sthaayi avastha tabhi hogi jab (E) nyoonatam ho. saankhyikeeya yaantriki ke anusaar (S) ek aisi raashi hai jo (E) ka nirantar vruddhi karanevaala ekadisht falan (monotonic function) hai. thos ka taap jab paramashoonya se aage badhta hai to saamya avastha ke dharm mein parivartan ki sambhaavana utpann hoti hai. thoson mein nimn taap par manibh roop dhaaran karne ki pravrutti pai jaati hai. taap jab ooaincha chadhta hai to (TS) pad ka prabhaav nimnalikhit mein se koi ek roop dhaaran kar sakta hai :

1. saamya sthitiyon ke chaturdik parmaanu dolan karne lag jaate hain. kramavyavastha ka yeh vyatikram sabhi thoson mein saarvabhaum roop se vyakt hota hai.

2. jaaleeya sanrachana mein aisa parivartan aa sakta hai ki paramaanuon ki adhik svatantrata praapt ho jaae. yeh parivartan apararoopeeya (allotropic) parivartan kahalaata hai. gandhak mein kai apararoopi parivartan hote hain.

3. jaaleeya sanrachana mein paramaanuon ke jodon ki adala-badli ke kaaran vyatikram ho sakta hai. mishradhaatuon mein praaya: yeh baat pai jaati hai.

4. aanavik manibhon tatha lavanon mein, jaise aimoniym kloraaid mein, jaaleeya sanrachana ka vyatikram vishisht anuon ya moolakon ke kaaran utpann ho sakta hai.

5. fir, jaaleeya sanrachana ke andar ki apni saamaanya sthiti se ikke-dukke parmaanu pravrajan kar antaraaleeya sthiti mein, ya satah par pahuainchane ke kaaran bhi, jaaleeya kram mein vyatikram utpann kar sakte hain. prayogon dvaara is baat ki sanpushti ki ja chuki hai ki visran tatha aayan chaalakata isi prakaar ke parivartan ke fal hain.

6. dravan tatha oordhvapaatan jaaleeya vyavastha ke charam vyatikram ke falasvaroop ghatit hote hain.

7. dhaatuon mein mukt ilektraun upasthit hote hain. chalishnuta unhein ooainche darje ki ooshmaachaalakata tatha vidyuchchaalakata pradaan karti hai.

inmein se koi bhi avyavastha (disoder) ooshmeeya oorja ka avashoshan kara sakti hai. avashoshit oorja hi vishisht ooshma pradaan karti hai, jisse taap mein vruddhi hoti hai ya fir vah gupt ooshma ka roop dhaaran kar leti hai.

thos ke pratyaasthi tatha plastic gun

prakruti mein paae jaanevaale thos poornat: drudh (rigid) naheen hote. bal ke lagne par inmein vikruti utpann ho jaati hai. bal hata lene par yadi vah pind apna poorvaroop grahan kar leta hai, tab ise pratyaasthi thos kehte hain. iske pratikool bal hata lene par yadi vah apni poorv aakruti dhaaran na kar sake to ise plastic kaheinge. ispaat aur rabar deergh seema ke bheetar pratyaasthi bane rahanevaale thos ke udaaharan hain, tatha poteen (putty) mein lagbhag praarambhik avastha se hi plaistik ke gun pradarshit hote hain. prati ikaai lanbaai mein utpann honevaali vikruti ko tanaav vikruti kehte hain, tatha prati ikaai lanbaai mein utpann honevaale sanpeedan ko sanpeedya vikruti kehte hain. pind mein prati ikaai kshetr par laganevaale bal ke maan ko pratibl kehte hain.

yadi ek aayataakaar nipind (block) a b s the ka falak b s kas diya jaae aur yadi iska viroopan a" b" s" the" aakruti mein kar diya jaae to is viroopan ko kartan (shear) kehte hain. thos ka pratyek parmaanu aakarshan aur pratikrshan balon ke madhya saamya avastha mein rahata hai. bal aaropit kiye jaane par ye parmaanu naveen sthitiyaaain praapt kar lete hain, tab ham kehte hain ki thos vikrut ho gaya.

pratyaasthata ki seema aaropit kiye jaanevaale pratibl ki prakruti, vikruti praapt karanevaale padaarth tatha iske poorv itihaas par nirbhar karti hai. taral sthaitik daab se bahut adhik vikruti utpann ki ja sakti hai.

kaaainch jaise amanibheeya thos nimn taap par bhangur ban jaate hain, kintu anek manibheeya thos, jaise dhaatueain, param shoonya taap ke nikat bhi prachur maatra mein tanyata ka pradarshan karte hain. anek thoson ke plaistik pravaah ka adhyayan kiya gaya hai. falasvaroop nimnalikhit mahatvapoorn niyam praapt hue hain :

1. khiskanevaale dharaatal ki seedh mein manibh ke vibhinn bhaagon ke aapekshik sthaanaantaran ke kaaran plaistik vikruti utpann hoti hai.

2. khiskanevaale dharaatal ki seedh mein sthaanaantaran hone ke liye upayukt dasha us dharaatal mein vightit honevaale kartan pratibl ke parinaam dvaara nirdhaarit hoti hai. saamaanyat: sthaanaantaran us samay hoga jab kartan pratibl ek nishchit kraantik kartan pratibl ke maan se adhik ho jaaega. plaistik vikruti ke ghatne ke saath kraantik kartan pratibl ka maan bhi badhta hai. is ghatna ki kaaryakathoreekaran (work hardening) kehte hain.

3. ek aisa nishchit taap hai jiske oopar taap badhne par kaarya kathoreekaran ka prabhaav vilupt ho jaata hai. is taap ko punarmrudukaran (softening) taap kehte hain. kraantik kartan pratibl ka maan punarmrudukaran taap ke neeche tak ke hi taap par nirbhar rahata hai.

dhaatuon ki uchch tanyata ka praadurbhaav unki apadravyata ke kaaran hota hai.

kvaantam yaantriki dvaara thos avastha ke siddhaant ka pratipaadan

san 1930 ke uparaant jab sanyoji ilektraun ke aacharan ke nirdhaaran ke liye kvaantam yaantriki ko prayukt kiya gaya to unheen dinon thos avastha ke siddhaant mein bhi vishesh pragati hui. thos sambandhi anusandhaan mein kvaantam yaantriki ka prayukt kiya jaana bahut kuchh vaisa hi hai jaisa maapaank (modular) pranaali ke liye.

jab ilektraunikeeya avastha ke tarangafalan (wave function) ka nirdhaaran karna hota hai to naabhik ke nideshaankon ko praachal (parameters) maankar chalte hain. baurn tatha openahaaimar ne hi ilektraunikeeya gati ko naabhikeeya gati se pruthak karne ki vidhi ka prachalan kiya tha. thos ke liye poorn tarangafalan atyadhik klisht hai.

nimnalikhit do vidhiyaaain us bhautik avastha ke liye upayukt hain jab ek ilektraun sanniktan ka upayog kiya jaaya :

1. paaramaanavik sannikt - ismein pratyek ilektraun ek diye hue naabhik se sambaddh rahata hai tatha sampoorn thos ka svaroop paramaanuon ya anuon ke ek samooh sa hota hai. is prakaar niroopit thos sadaiv hi ek achaalak (ya pruthakkaari / insulater) hota hai.

2. mukt ilektraun sanniktan - is niroopan mein maan liya jaata hai ki pratyek sanyoji ilektraun jaaleeya vyavastha mein svatantr roop se vichran karta hai. is prakaar tarangafalan ka aayaam parimit ho jaata hai. yeh vidhi sabhi chaalakon tatha ardhachaalakon aur achaalakon ki badi sankhya ke liye laagoo hoti hai.

thos ke gunadharm ka pratipaadan

kvaantam yaantriki ki vidhiyaaain thos ke gunon ke beech paarasparik sambandh sthaapit karne ke liye vistrut roop se prayukt hoti hai. inmein se nimnalikhit vishesh ullekhaneeya hain :

(k) sansrujan thos ki sansanjan oorja ko is prakaar vyakt kar sakte hain ki yeh vah oorja hai jo thos satah se kisi ilektraun ki anant tak le jaane mein vyaya hogi, arthaat oorvapaatan ki ooshma ke baraabar. yadi ilektraun ki oorja gyaat ho to sansanjan oorja ka maan praapt kar sakte hain. yeh vidhi vibhinn thoson ki aapekshik sansanjan oorja ka maan gyaat karne ke liye bahutaayat se kaam mein laai jaati hai.

(kh) vidyutchchaalakata thos mein vidyut ka sanchaalan mukt ilektraun, ya chal aayanon, ki upasthiti ke kaaran hota hai. kvaantam yaantriki ki sabse badi safalta is baat mein hai ki dhaatuon aur ardhachaalakon mein ilektrauneeya chaalakata ki prakruti iske dvaara theek-theek samajhi ja saki hai, kintu nimn taap par pradarshit honevaali atichaalakata ke gun ki vyaakhya abhi tak kvaantam yaantriki ke aadhaar par naheen ki ja saki hai. yeh is kaaran hai ki tarangasameekaran ke parishuddh hal abhi tak sambhav naheen ho sake hain.

(g) chunbakeeyata ke gun kvaantam yaantriki ka vistrut upayog chunbakeeya gunon ki vyaakhya tatha unke anusandhaan ke nimitt kiya gaya hai. visham chunbakeeya, samachunbakeeya, tatha lohachunbakeeya padaarthon ke gunon ki bhi poorn roop se vyaakhya ki ja saki hai.

(gh) prakaasheeya gun thos ke anek prakaashakeeya gunon ki, jo kuchh dinon poorv tak rahasyapoorn bane hue the, ab kvaantam yaantriki ke aadhaar par sahi vyaakhya ki ja saki hai. dhaatuon ke adhyayan mein bhi sarvaadhik pragati sambhav ho saki hai. mukt ilektraun ke siddhaant par svarn, taaainba tatha peetal sareekhi mishradhaatuon ke varn ki samuchit vyaakhya ki ja saki hai. kvaantam yaantriki dvaara is baat ka samaadhaan praapt ho saka hai ki kshaar dhaatueain varnakram (spectrum) ke paraabaingani bhaag mein paaradarshita ka gun kyon pradarshit karti hain.

baahari kadiyaaain