Question

A 50W bulb emits light of wavelength 400nm. Calculate number of photons emitted by the bulb per second.

Answer 1

Answer:

Given:

Power (P) = 50 W

Wavelength (λ) = 400 nm

To Find:

Number of photons emitted by the bulb per second

Solution:

Energy of isolated photon is calculated by

$\green{\boxed{\rm E = \dfrac{hc}{\lambda} }}$

Where,

h = 6.63 × 10⁻³⁴

c = 3 x 10⁸

λ = 400 nm = 4 x 10⁻⁷ m

Substituting the above values in formula,

We get,

$\rm \implies E = \dfrac{(6.63 \times 10^-34) \times (3 \times 10^8)}{4 \times 10^-7}$

$\purple{\implies \rm E = 4.97 \times 10^-19}$

No of photons emitted per unit time is calculated by

$\red{\boxed{\rm N = \dfrac{P}{E} }}$

Where,

P = 50 W

E = 4.97 x 10⁻¹⁹

Substituting the above values in formula,

We get,

$\implies \rm N = \dfrac{50}{4.97 \times 10^-19}$

$\implies \rm N = 10.06 \times 10^1^9$

$\orange{\implies \rm N = 1.0 \times 10^2^0}$

Hence,

1 x 10²⁰

Photons are emitted by the bulb per second