Photon properties — E = hf, p = h - λ — Hinglish notes

2.3.3 · Physics › Modern Physics

Photon KYA hota hai?

Yeh idea exist kyun karta hai? Classical physics kehta tha ki kisi bhi frequency ki wave koi bhi amount mein energy continuously carry kar sakti hai. Lekin experiments (blackbody radiation, photoelectric effect) ne dikhaya ki energy fixed chunks mein exchange hoti hai jo frequency ke proportional hain. Planck aur Einstein ne ise resolve kiya yeh keh kar ki energy khud packaged hoke aati hai.

$E = h f$ ko first principles se derive karna

Hum yahan KAISE pahunchte hain (logic chain):

Planck ka quantization (1900): blackbody radiation explain karne ke liye, Planck ne assume kiya ki ek wall ke oscillators sirf un energies mein ho sakte hain jo ek quantum ke integer multiples hain: $E_{n} = nh f$ . Sabse chhota exchangeable chunk $h f$ hai.
Einstein ki leap (1905): light field khud inhi chunks se bani hai. Ek photon = ek quantum = energy $h f$ .
Wave relation $c = f λ$ use karke, substitute karo $f = c / λ$ : $E = h f = h \cdot \frac{c}{λ} = \frac{h c}{λ} .$

$p = h / λ$ ko first principles se derive karna

Photon ki zero rest mass hoti hai, isliye hum $p = m v$ use nahi kar sakte. Hum full relativistic energy–momentum relation use karte hain:

KAISE:

$m_{0} = 0$ set karo (photon ki rest mass nahi hoti): $E^{2} = (p c)^{2} ⟹ E = p c ⟹ p = \frac{E}{c} .$
Ab $E = h f$ plug in karo: $p = \frac{h f}{c} .$
$c = f λ \Rightarrow f / c = 1/ λ$ use karo: $p = \frac{h}{λ}$

Figure — Photon properties — E = hf, p = h - λ

Worked Examples

Common Mistakes (Steel-manned)

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

Socho light paani ki tarah nahi, sikkon ki tarah deliver hoti hai. Paani aap kisi bhi amount mein daal sakte ho; sikke fixed values mein aate hain. Ek blue-light ka sikka red-light ke sikke se zyada valuable hota hai — "value" color (frequency) par depend karti hai, na ki kitne sikke hain. Aur bhale hi har sikke ka weight kuch na ho, jab unki poori stream ek wall se takrati hai tab bhi woh ise thoda dhakka deti hai — woh dhakka photon ka momentum hai. Zyada sikke (zyada bright light) = bada total dhakka, lekin har sikke ki value aur push uske color se fixed hai.

Flashcards

Photon kya hota hai?

EM field ka quantum — ek massless particle jo

c

par move karta hai, energy

h f

aur momentum

h / λ

ke saath.

Frequency ke terms mein photon energy ka formula?

E = h f

Wavelength ke terms mein photon energy ka formula?

E = h c / λ

Photon energy amplitude par nahi, frequency par kyun depend karti hai?

Ek single photon ka koi "amplitude" nahi hota; frequency hi photons ko distinguish karti hai, isliye energy

f

ke saath scale karni chahiye. Amplitude = photons ki sankhya.

p = h / λ

derive karo.

E^{2} = (p c)^{2} + (m_{0} c^{2})^{2}

m_{0} = 0

ke saath

E = p c

milta hai, isliye

p = E / c = h f / c = h / λ

Ek massless photon mein momentum kyun ho sakta hai?

Kyunki

p = m v

sirf non-relativistic hai; sach mein relation

E = p c

hai jo

m_{0} = 0

par bhi nonzero

p

deta hai.

Ek photon ke liye

E

aur

p

ko link karne wala relation?

E = p c

Agar wavelength double ho jaaye, toh

E

aur

p

ka kya hoga?

Dono aadhe ho jaate hain (dono

\propto 1/ λ

Planck's constant ki value?

h = 6.626 \times 1 0^{- 34}

J·s.

Laser se per second emit hone wale photons kaise nikalte hain?

Power ko energy per photon se divide karo:

N = P / (h c / λ)

500 nm photon ki energy eV mein (approx)?

~2.48 eV.

Connections

Photoelectric Effect — threshold frequency explain karne ke liye $E = h f$ use karta hai.
Planck's Law and Blackbody Radiation — $E = h f$ ka origin.
de Broglie Wavelength — matter waves ke liye $p = h / λ$ ko ulta chalata hai.
Compton Effect — direct proof ki photons $h / λ$ momentum carry karte hain.
Relativistic Energy-Momentum Relation — $E = p c$ ka source.
Radiation Pressure — photon momentum ka macroscopic consequence.
Wave-Particle Duality — woh bada picture jisme yeh note fit hota hai.