2.3.15 · D1Spectral series — Lyman, Balmer, Paschen
Ek hydrogen atom bilkul waise hai jaise ek ball ek staircase ke fixed steps mein se kisi ek pe aaram kar rahi ho; jab ball kisi neeche wale step pe girti hai to ek flash of light nikalti hai jiska colour poori tarah se iss baat pe depend karta hai ki wo kitni door giri . Kyunki step heights fixed hain, hydrogen hamesha same set of colours mein glow karti hai — aur ye page ek ek symbol karke, ek ek vocabulary piece build karta hai jo tumhe wo story padhne ke liye chahiye.
Isse pehle ki tum parent note pe trust kar sako, tumhe har wo symbol pehle se samajh aana chahiye jo wo tumhare saamne daalta hai. Neeche, har symbol ko tab introduce kiya gaya hai jab uske pehle wala symbol already explain ho chuka ho. Upar se neeche padho — kuch bhi use se pehle use nahi hoga jab tak wo build na ho jaye.
Intuition Figures ki numbering kaise hoti haiIs page pe teen figures hain, jinhe Figure 1 (s01) , Figure 2 (s02) , Figure 3 (s03) label kiya gaya hai. Har ek figure us section ke bilkul baad aata hai jise uski zaroorat hai, aur text hamesha usse explicitly name karta hai. Jab tum "Figure 1" padho, to s01 tag wali picture tak scroll karo.
Definition Electron aur uski orbitElectron wo choti si negatively-charged particle hai jo atom ke centre ke around chakkar lagati hai. Picture mein, ye wo choti si dot hai jo nucleus ke around ek ring pe move karti hai — nucleus wo heavy central core hai jo positive hota hai. Jis ring pe ye baith ti hai use orbit kehte hain — socho "building ki kaun si floor pe electron rehta hai".
Figure 1 (s01) — atom ki rings.
Hum ye picture kyun dekhte hain? Kyunki poora topic is baat pe hai ki electron kaun si ring pe rehta hai ye change karta hai . Agar tum rings nahi dekh sakte, to baaki sab sirf symbols hain. In rings ke baare mein sab kuch Bohr Model of the Atom se aata hai.
n n counting label hai: n = 1 n = 2 n = 3 n = 1 , 2 , 3 , … 1.5 0 Picture: rings ko andar se bahar ki taraf number karo. n
Whole number kyun hota hai, koi bhi number kyun nahi? Kyunki electron rings ke beech mein baithne ki permission nahi hai — ek rule jo quantization kehlata hai (dekho Quantization of Angular Momentum ). Yahi "sirf whole steps allowed hain" wali baat hydrogen ko sharp, alag alag colours produce karne ka reason hai, naki ek smear.
Intuition Steps upar ki taraf squish kyun hote hainFigure 1 (s01) dekho: neeche wali rings door door hain, upar wali rings paas paas crowd karti hain. To bottom ke paas ki jump ek badi energy drop cover karti hai, aur top ke paas ki jump ek choti si drop cover karti hai. Ise yaad rakho — ye baad mein har wavelength ordering explain karta hai.
E E n Energy ka matlab hai "kitni oomph" kisi cheez mein hai — yahan, kitni strongly electron nucleus se bound hai. E n n n subscript hai: ye sirf batata hai ki ye energy kis ring ki hai. E 2 Picture: energy staircase pe har step ki height.
Definition Unit "eV" (electron-volt)Itni choti energies ko electron-volts mein measure karte hain, likha jata hai eV eV eV Photon Energy and Planck's Relation .
Common mistake "Higher floor = zyada energy, toE n Kyun sahi lagta hai: seedhiyan chadhna sach mein zyada mehnat leta hai, to upar wala bada number hona chahiye.
Trap: numbers negative hain. Rule se, E 1 = − 13.6 eV E 2 = − 3.4 eV − 3.4 − 13.6 zyada hai, higher floor mein sach mein zyada energy hai — lekin number chota lagta hai kyunki wo kam negative hai.
Fix: ise zero se neeche temperature ki tarah padho: − 3 ∘ − 1 3 ∘ zyada garam hai. Minus sign ka matlab hai "bound"; E = 0
Photon light ka ek single particle-packet hai. Jab electron ek floor neeche girta hai, exactly ek photon paida hota hai, wo energy le jaata hai jo lose hui thi.
Picture: atom se nikalta ek wavy arrow — bilkul wohi squiggle jiske shape ko hum Figure 2 (s02) mein zoom in karte hain, jo neeche hai.
λ λ ek wave ki length hai — ek crest se agli crest tak ki distance. Chota λ λ Picture: squiggle ke do crests ke beech ka gap.
Figure 2 (s02) — wavelength kya hoti hai.
Hum λ λ measure karta hai — ye observable colour hai. Energy cause hai; λ
c ν h
c speed of light hai — ek fixed constant, c ≈ 3.00 × 1 0 8 m/s ν frequency hai: ek second mein kitne wave-crests guzarte hain, s − 1 h Planck's constant hai, h ≈ 6.63 × 1 0 − 34 J⋅s = 4.14 × 1 0 − 15 eV⋅s
Tool "h c / λ Humare paas ek wavelength hai (jo hum dekhte hain) lekin hum ek energy chahte hain (jo cause hua). Yahi ek equation dono ke beech exact bridge hai — yahi puri reason hai ki ek fixed energy drop ek fixed colour deta hai. Ye Photon Energy and Planck's Relation ka dil hai.
Dono constants multiply karo: h c = ( 4.14 × 1 0 − 15 eV⋅s ) ( 3.00 × 1 0 8 m/s ) ≈ 1.24 × 1 0 − 6 eV⋅m = 1240 eV⋅nm λ ( nm ) = E ( eV ) 1240
Kuch bhi combine karne se pehle, triangle symbol se milte hain. Δ "change in" ya "difference of" ke liye. To Δ E
Δ E Δ Δ E positive aaye — ye drop ki size hai, wo energy jo photon ko di jaati hai — to is page pe hum deliberately "upar wala minus neeche wala" likhte hain:
Δ E = E n 2 − E n 1 ( n 2 > n 1 ) E n 2 E n 1 zyada hai, ye difference ek positive number hai.
Kyun textbook ka "final minus initial" order nahi? Bahut si books mein Δ E = E final − E initial fall ke liye negative hota hai (energy lost). Ye bookkeeping ke liye theek hai, lekin yahan hum sirf emitted light ki magnitude ki parwah karte hain, isliye hum wo order choose karte hain jo Δ E n 1 2 1 − n 2 2 1 Picture: Figure 3 (s03) mein start floor se landing floor tak ke arrow ki vertical height.
Figure 3 (s03) — n 2 n 1
Do alag labels kyun rakhte hain? Kyunki landing floor n 1 starting floor n 2
1/ λ λ 1 wavelength se ek divided — literally "ek metre mein kitni waves fit hoti hain". Bada 1/ λ m − 1 Ise flip kyun karte hain? Kyunki energy 1/ λ proportional hai, λ 1/ λ
Definition Rydberg constantR H R H R H ≈ 1.097 × 1 0 7 m − 1 13.6 eV h c H Hydrogen ke liye hai — sirf ek electron.
Z Z protons ki sankhya hai, jise atomic number bhi kehte hain. Hydrogen mein Z = 1 He + Z = 2 hydrogen-like ion hai. Bada Z Z 2 λ 1 = R H Z 2 ( n 1 2 1 − n 2 2 1 ) Z 2 Hydrogen-like Ions and Z dependence ka poora point hai. Plain hydrogen ke liye Z = 1 Z 2 = 1
Ab jab har symbol build ho gaya hai, parent ka master equation plain words mein padha jaata hai:
waves per metre λ 1 = fixed number R H landing floor n 1 2 1 − start floor n 2 2 1
Agar electron ko itni energy milti hai ki wo staircase ke top se pare ja sake, to wo atom ko bilkul chod deta hai — atom ionized ho jaata hai. Ye tab hota hai jab n → ∞ E n → 0 ionization energy kehte hain, 13.6 eV Ionization Energy ).
Picture: Figure 1 (s01) ke top pe dashed "escape line".
n 2 → ∞ → ∞ 1/ n 2 2 → 0 series limit deta hai — series ki sabse choti wavelength, ek electron se jo bilkul azaadi ke kinare se girta hai.
Energy level E_n equals minus 13.6 over n squared
Photon and wavelength lambda
Photon energy hc over lambda
Photon energy equals delta E
Wavenumber and Rydberg R_H
Ionization and series limit
Charge Z scaling for ions
Aise padho: orbits floor number n E n barabar hoti hai; us energy ko wavelength mein convert karke aur landing floor ke hisaab se group karke named series milti hain, Z
Right side chhupao aur khud test karo. Agar koi bhi jawab tumhe surprise kare, to parent note se pehle wo section dobara padho.
E n "kaun si ring/floor", n = 1 , 2 , 3 , …
E n E n = − 13.6 eV / n 2
E n electron bound hai; E = 0
Kaun sa bada hai, E 1 = − 13.6 E 2 = − 3.4 E 2
Photon kya hai light ka ek single packet jo electron ke girne par emit hota hai
λ ek wave ki length; chota = high energy, bada = low energy
Δ "change in" / "difference of"
Is page pe Δ E E n 2 − E n 1
Photon ko drop se kaun sa equation link karta hai E photon = Δ E
Ek fall mein n 1 n 2 n 1 n 2
Wavelength ko energy se kaun sa equation link karta hai E = h c / λ
c h c ≈ 3.00 × 1 0 8 m/s h ≈ 6.63 × 1 0 − 34 J⋅s
Fast eV-to-nm shortcut λ ( nm ) = 1240/ E ( eV )
λ 1/ λ energy 1/ λ
R H Rydberg constant for hydrogen, 1.097 × 1 0 7 m − 1
Z nucleus mein protons ki sankhya (atomic number); hydrogen ke liye Z = 1
One-electron ion ke liye formula kaise badlega Z 2
n 2 → ∞ electron ionization edge se girta hai → series limit
Ionization kya hai electron atom se poori tarah nikal jaata hai; E n → 0 n → ∞
Bohr Model of the Atom — jahan se quantized rings aur E n = − 13.6/ n 2 Quantization of Angular Momentum — n Photon Energy and Planck's Relation — §5 mein build hua E = h c / λ Ionization Energy — staircase ka top aur series limit.Hydrogen-like Ions and Z dependence — R H Z 2 Emission vs Absorption Spectra — falls emit karte hain, climbs absorb karte hain; same floors, opposite arrows. 
