Q: The energy of a single photon (quantum) of light of frequency ν is:

E = h\nu. The energy of a photon is E = hν, where h is Planck's constant.

Q: The energy of a photon of wavelength 600 nm is approximately (h = 6.6 × 10⁻³⁴ J s, c = 3 × 10⁸ m/s):

3.3 \times 10^{-19} J. E = hc/λ = (6.6 × 10⁻³⁴ × 3 × 10⁸)/(600 × 10⁻⁹) = 3.3 × 10⁻¹⁹ J.

Q: A source emits light of wavelength 500 nm at a power of 1 W. Approximately how many photons does it emit per second? (Take photon energy ≈ 4 × 10⁻¹⁹ J)

2.5 \times 10^{18}. Number per second = Power ÷ energy per photon = 1 ÷ (4 × 10⁻¹⁹) = 2.5 × 10¹⁸ photons/s.

Question 1

According to Planck's quantum theory, light energy is emitted or absorbed:

Accepted Answer

In discrete packets called quanta (photons). Planck proposed that radiant energy is emitted or absorbed only in discrete packets (quanta), each of energy E = hν.

Question 2

The energy of a single photon (quantum) of light of frequency ν is:

Accepted Answer

E = h
u. The energy of a photon is E = hν, where h is Planck's constant.

Question 3

Planck's quantum theory was originally proposed to explain:

Accepted Answer

The spectrum of black-body radiation. Planck introduced energy quantisation to correctly explain the black-body radiation spectrum, which classical wave theory could not.

Question 4

In terms of wavelength λ, the energy of a photon is:

Accepted Answer

E = \dfrac{hc}{\lambda}. Since ν = c/λ, the photon energy is E = hν = hc/λ — inversely proportional to wavelength.

Question 5

The momentum of a photon of wavelength λ is:

Accepted Answer

p = \dfrac{h}{\lambda}. A photon has momentum p = h/λ = E/c, even though its rest mass is zero.

Question 6

The rest mass of a photon is:

Accepted Answer

Zero. A photon has zero rest mass; it always moves at speed c and carries energy hν and momentum h/λ.

Question 7

The energy of a photon of wavelength 600 nm is approximately (h = 6.6 × 10⁻³⁴ J s, c = 3 × 10⁸ m/s):

Accepted Answer

3.3 	imes 10^{-19} J. E = hc/λ = (6.6 × 10⁻³⁴ × 3 × 10⁸)/(600 × 10⁻⁹) = 3.3 × 10⁻¹⁹ J.

Question 8

Two photons have wavelengths in the ratio 1 : 2. The ratio of their energies is:

Accepted Answer

2 : 1. E ∝ 1/λ, so if λ₁ : λ₂ = 1 : 2 then E₁ : E₂ = 2 : 1 (the shorter wavelength has more energy).

Question 9

Planck's quantum idea, together with Einstein's work, established that light has:

Accepted Answer

A dual (wave and particle) nature. The quantum (photon) picture, alongside the wave behaviour in interference/diffraction, shows that light exhibits wave–particle duality.

Question 10

A source emits light of wavelength 500 nm at a power of 1 W. Approximately how many photons does it emit per second? (Take photon energy ≈ 4 × 10⁻¹⁹ J)

Accepted Answer

2.5 	imes 10^{18}. Number per second = Power ÷ energy per photon = 1 ÷ (4 × 10⁻¹⁹) = 2.5 × 10¹⁸ photons/s.

Question 11

The energy of a photon of wavelength 300 nm is (h = 6.6 × 10⁻³⁴ J s, c = 3 × 10⁸ m/s):

Accepted Answer

6.6 × 10⁻¹⁹ J. E = hc/λ = (6.6 × 10⁻³⁴ × 3 × 10⁸)/(300 × 10⁻⁹) = 6.6 × 10⁻¹⁹ J.

Question 12

The momentum of a photon of wavelength 660 nm is (h = 6.6 × 10⁻³⁴ J s):

Accepted Answer

1 × 10⁻²⁷ kg·m/s. p = h/λ = 6.6 × 10⁻³⁴/(660 × 10⁻⁹) = 1 × 10⁻²⁷ kg·m/s.

Question 13

A photon has energy 3.96 × 10⁻¹⁹ J. Its frequency is (h = 6.6 × 10⁻³⁴ J s):

Accepted Answer

6 × 10¹⁴ Hz. ν = E/h = 3.96 × 10⁻¹⁹/6.6 × 10⁻³⁴ = 6 × 10¹⁴ Hz.

Question 14

Two photons have wavelengths in the ratio 2 : 3. The ratio of their energies is:

Accepted Answer

3 : 2. E ∝ 1/λ, so E₁ : E₂ = 3 : 2.

Question 15

A 3.3 W monochromatic source emits photons of energy 3.3 × 10⁻¹⁹ J each. The number of photons emitted per second is:

Accepted Answer

1 × 10¹⁹. N = P/E = 3.3/(3.3 × 10⁻¹⁹) = 1 × 10¹⁹ per second.

Question 16

The energy of a 400 nm photon in electron-volts is (hc ≈ 1240 eV·nm):

Accepted Answer

3.1 eV. E = 1240/λ(nm) = 1240/400 = 3.1 eV.

Question 17

A photon of energy 3 × 10⁻¹⁹ J has momentum (c = 3 × 10⁸ m/s):

Accepted Answer

1 × 10⁻²⁷ kg·m/s. p = E/c = 3 × 10⁻¹⁹/3 × 10⁸ = 1 × 10⁻²⁷ kg·m/s.

Question 18

Two photons have frequencies in the ratio 3 : 1. The ratio of their energies is:

Accepted Answer

3 : 1. E = hν ∝ ν, so E₁ : E₂ = 3 : 1.

Max Planck's Quantum Theory — JEE Main Physics MCQs with Solutions

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