Bohr atomic model and electron shells — Hinglish notes

1.3.1 · Hardware › Materials & Atomic Structure

YEH model exist kyun karta hai?

Hardware ke liye YEH kyun matter karta hai: semiconductors, conductors, insulators, doping, aur band gaps ke baare mein sab kuch yahan se shuru hota hai. Silicon conduct karega ya nahi yeh depend karta hai ki electrons shells mein kaise baithe hain aur outer wale electrons ko bahar nikalne ke liye kitni energy chahiye.

Postulates KYA hain?

Orbit radius aur energy KAISE derive karein (scratch se)

Hum ek hydrogen atom consider karte hain: ek electron (charge $- e$ ) ek proton (charge $+ e$ ) ke around orbit karta hai.

Step 1 — Force balance (KYU: electron ko circle mein rakhna)

Electrostatic (Coulomb) attraction centripetal force supply karta hai:

$\frac{1}{4 π ε _{0}} \frac{e ^{2}}{r ^{2}} = \frac{m v ^{2}}{r}$

Yeh step kyun? Ek circular orbit ko ek inward force $m v^{2} / r$ chahiye; yahan sirf inward force Coulomb pull hai, toh dono equal hone chahiye.

Step 2 — Quantization (KYU: yeh Bohr ka naya rule hai)

$m v r = n ℏ \Rightarrow v = \frac{n ℏ}{m r}$

Yeh step kyun? Postulate 3 restrict karta hai ki kaun si orbits allowed hain. Iske bina hume $r$ ki continuous range milti.

Step 3 — $v$ ko eliminate karke radius nikalo

$v$ ko Step 1 mein substitute karo:

$\frac{1}{4 π ε _{0}} \frac{e ^{2}}{r ^{2}} = \frac{m}{r} (\frac{n ℏ}{m r})^{2} = \frac{n ^{2} ℏ ^{2}}{m r ^{3}}$

Cancel karo aur $r$ ke liye solve karo:

$r_{n} = \frac{4 π ε _{0} ℏ ^{2}}{m e ^{2}} n^{2}$

Step 4 — Total energy

Kinetic $K E = \frac{1}{2} m v^{2}$ . Step 1 use karke, $m v^{2} = \frac{1}{4 π ε _{0}} \frac{e ^{2}}{r}$ , toh $K E = \frac{1}{8 π ε _{0}} \frac{e ^{2}}{r}$ . Potential $P E = - \frac{1}{4 π ε _{0}} \frac{e ^{2}}{r}$ (negative: bound hai).

$E = K E + P E = \frac{1}{8 π ε _{0}} \frac{e ^{2}}{r} - \frac{1}{4 π ε _{0}} \frac{e ^{2}}{r} = - \frac{1}{8 π ε _{0}} \frac{e ^{2}}{r}$

Negative kyun? Bound systems ki total energy negative hoti hai — electron ko free karne ke liye tumhe energy add karni padti hai.

$r_{n}$ insert karo:

$E_{n} = - \frac{m e ^{4}}{8 ε _{0}^{2} h ^{2}} \frac{1}{n ^{2}} = - \frac{13.6 eV}{n ^{2}}$

Step 5 — Spectral lines (light emission)

Jab electron $n_{i} \to n_{f}$ drop karta hai:

$h f = E_{n_{i}} - E_{n_{f}} = 13.6 eV (\frac{1}{n _{f}^{2}} - \frac{1}{n _{i}^{2}})$

Yeh observed hydrogen spectrum ko reproduce karta hai — yahi woh win hai jisne is model ko famous banaya.

Figure — Bohr atomic model and electron shells

Electron shells aur capacity (Hardware wala part)

Worked examples

Common mistakes (steel-manned)

Active recall

Recall Khud ko test karo (answers chhupaao)

Electron ko orbit mein kaun si force rakhti hai? → Coulomb (electrostatic) attraction.
Bohr's model mein kaun si quantity quantized hai? → Angular momentum, $L = n ℏ$ .
Allowed radii ka formula? → $r_{n} = a_{0} n^{2}$ .
Hydrogen mein level $n$ ki energy? → $- 13.6/ n^{2}$ eV.
Shell $n$ mein max electrons? → $2 n^{2}$ .
Conductivity kya determine karta hai? → Valence electrons ki number.

Recall Feynman: ek 12-year-old ko explain karo

Socho ek staircase hai. Ek ball step 1, step 2, step 3 par baith sakti hai — lekin steps ke beech floating nahi. Ek electron woh ball hai; steps shells hain. Yeh kisi bhi step par hamesha ke liye quietly baith sakta hai. Upar step jaane ke liye use bilkul sahi amount ki energy khaani padti hai; jab yeh ek step neeche girta hai toh ek exact color ki light ki flash emit karta hai. Isliye garam atoms specific colors mein glow karte hain, na ki har color mein — har color ek electron ka ek specific set of steps pe hop karna hai.

Connections

Atomic structure and the periodic table — shells periods & groups explain karte hain.
Valence electrons and bonding — outer shell → covalent/ionic/metallic bonds.
Energy bands in solids — crystals mein shells bands mein broaden ho jaate hain.
Semiconductors and the band gap — Si (4 valence e⁻) partially conduct kyun karta hai.
Conductors insulators and doping — direct Hardware application.
Quantum mechanical model of the atom — successor jo Bohr ke flaws fix karta hai.

What force provides the centripetal force in the Bohr model?

Nucleus (positive) aur electron (negative) ke beech Coulomb (electrostatic) attraction.

What is Bohr's quantization condition?

Angular momentum quantized hai:

L = m v r = n ℏ

, jahan

n = 1, 2, 3, \dots

Formula for the radius of the

n

th Bohr orbit?

r_{n} = a_{0} n^{2}

jahan

a_{0} \approx 0.529

Å Bohr radius hai.

Energy of the

n

th level of hydrogen?

E_{n} = - 13.6/ n^{2}

eV.

Why is the total energy of a bound electron negative?

Kyunki electron ko free (ionize) karne ke liye energy add karni padti hai; potential energy kinetic energy par dominate karti hai.

Maximum number of electrons in shell

n

2 n^{2}

(K=2, L=8, M=18, N=32).

What are valence electrons and why do they matter?

Outermost shell mein electrons; yeh bonding aur electrical conductivity control karte hain.

How many valence electrons does silicon have, and what does that make it?

4 valence electrons → ek semiconductor.

When does a Bohr atom emit light?

Sirf jab ek electron higher orbit se lower orbit mein jump karta hai,

Δ E = h f

energy ka photon emit karke.

Photon energy for an

n = 3 \to 2

jump in hydrogen?

E_{3} - E_{2} = - 1.51 - (- 3.4) = 1.89

eV (H-alpha, red).

n \to \infty

, what happens to

E_{n}

E_{n} \to 0

; electron free ho jaata hai (atom ionized ho jaata hai).

Which classical prediction did Bohr's model overturn?

Yeh ki ek orbiting (accelerating) electron continuously radiate karta hai aur nucleus mein spiral ho jaata hai.