Photoelectric effect — Einstein's photon model

2.1.2 · Chemistry › Quantum Atomic Structure

Photoelectric effect KYA hai?

4 experimental facts jo classical wave theory explain NAHI kar sakti thi:

Ek ==threshold frequency $ν_{0}$ == hoti hai: usse neeche, koi electron emit nahi hota, chahe light kitni bhi intense kyun na ho.
$ν_{0}$ ke upar, emission instantaneous hoti hai (koi time delay nahi), chahe light dim hi kyun na ho.
Nikle hue electrons ki kinetic energy frequency par depend karti hai, intensity par nahi.
Intensity sirf electrons ki sankhya (current) badlati hai, unki energy nahi.

Einstein ne isse KAISE fix kiya — photon model

Einstein (1905) ne Planck ka quantum idea liya aur use physical bana diya: light khud quantized hoti hai energy ke packets mein jinhein photons kehte hain.

Photoelectric equation first principles se derive karna

EK electron ke liye energy ka hisaab-kitaab:

Photon $h ν$ energy deliver karta hai. Electron ko pehle metal surface se escape karne ke liye ek "toll pay" karni padti hai — ye minimum escape energy work function $ϕ = h ν_{0}$ hai. Jo bacha woh kinetic energy ban jaata hai:

$energy in h ν = cost to escape ϕ + energy left over K E_{m a x}$

Rearrange karne par:

$K E_{m a x}$ kyun, sirf $K E$ kyun nahi? Metal ke andar deeper electrons bahar aate waqt extra energy lose karte hain, isliye woh slower emerge karte hain. Maximum KE usi surface electron ki hoti hai jo sirf minimum toll $ϕ$ pay karta hai.

Stopping potential

$K E_{m a x}$ measure karne ke liye, ek reverse voltage lagao jab tak current bilkul band na ho jaaye. Electron us voltage ko climb karte waqt apni saari KE kho deta hai:

$K E_{m a x} = e V_{0}$

Photoelectric equation ke saath combine karo:

$e V_{0} = h ν - ϕ \Rightarrow V_{0} = \frac{h}{e} ν - \frac{ϕ}{e}$

Ye ek straight line hai $V_{0}$ vs $ν$ ki, slope $h / e$ ke saath — ek graph se Planck's constant measure karne ka tarika!

Figure — Photoelectric effect — Einstein's photon model

Worked Examples

Forecast-then-Verify

Recall Padhne se pehle forecast karo

Q: Tum light ki intensity double karte ho lekin frequency fixed rakhte ho ( $ν_{0}$ ke upar). (a) electrons ki sankhya, (b) unka $K E_{m a x}$ , (c) stopping potential — kya hoga?

Verify: (a) double hoti hai — zyada photons ⇒ zyada electrons. (b) unchanged — har photon abhi bhi $h ν$ carry karta hai. (c) unchanged — $V_{0}$ sirf $K E_{m a x}$ par depend karta hai, isliye $ν$ par.

Common Mistakes (Steel-manned)

Active Recall

Ejection ke baad ek photon ki energy kin do chezon mein split hoti hai?

Work function

ϕ

(escape cost) aur electron ki

K E_{m a x}

mein.

Einstein's photoelectric equation batao.

K E_{m a x} = h ν - ϕ = h (ν - ν_{0})

Koi bhi electron eject hoga ya nahi, ye kya decide karta hai?

Frequency: use threshold frequency

ν_{0}

se zyada hona chahiye (yaani

h ν > ϕ

Intensity badhane se kya badalta hai?

Ejected electrons ki sankhya (photocurrent), unki kinetic energy NAHI.

Work function aur threshold frequency ka kya relation hai?

ϕ = h ν_{0}

Stopping potential ka

K E_{m a x}

se kya relation hai?

e V_{0} = K E_{m a x}

, isliye

V_{0} = K E_{m a x} / e

V_{0}

ν

graph ki slope kya hai?

h / e

(Planck's constant measure karne ke liye use hoti hai).

eV·nm mein photon energy ke liye handy shortcut?

E (eV) = 1240/ λ (nm)

Classical wave theory kyun fail hoti hai?

Ye predict karti hai ki energy time ke saath accumulate hoti hai aur intensity par depend karti hai, jabki experiment mein instantaneous, frequency-dependent emission hoti hai.

Threshold wavelength ka formula?

λ_{0} = h c / ϕ

Recall Feynman: ek 12-saal ke bachche ko explain karo

Ek claw machine imagine karo jahan har coin light ka ek chhota packet hai. Ek toy jeetne ke liye (ek electron kick out karne ke liye) tumhare paas ek aisi coin honi chahiye jo kam se kam ek certain amount ki ho. Agar teri coin chhoti hai (light zyada red hai), toh tum ek million chhoti coins daal sakte ho aur phir bhi kuch nahi jeetoge — ek coin, ek try. Agar teri coin kaafi badi hai (light kaafi blue hai), toh tum turant jeetto, aur jo bhi change bachti hai wahi decide karta hai ki toy kitni tez bahar aati hai. Zyada same size ki coins daalna zyada toys jeetta hai, faster toys nahi.

Connections

Planck's Quantum Theory — jahan $E = h ν$ janam hua (black-body radiation).
Wave-Particle Duality — photon light ki particle nature ke roop mein; de Broglie ise matter tak extend karta hai.
Work Function and Binding Energy — same idea Photoelectron Spectroscopy mein bhi aata hai.
Bohr Model of the Atom — light ke saath quantized energy exchange (absorption/emission).
Compton Effect — aur proof ki photons momentum carry karte hain, sirf energy nahi.
Electromagnetic Spectrum — kyun UV electrons eject karta hai lekin red light aksar nahi kar sakti.