Question

A 66.26 watt bulb emits radiation of wavelength
100 nm. If only 60% of energy emitted in the form
radiations then the number of quanta emitted by tt
bulb per second is
(1) 2 x 1020
(2) 3 x 1018

(3) 2 x 1019
(4) 4 1017

Answer 1

Answer:

Power of the bulb = 66.26 Watt

Since power is defined as work done per unit time, so, a 66.26 W bulb will emit 66.26 J of energy per second.  

∴ Energy, E = 66.26 J

Here, we are given that only 60% of energy is emitted in the form of radiations.

∴ Final energy emitted, E = [66.26 * 60/100] J

Let the no. of quanta emitted by the bulb per second be “x”.

Now, we can write the equation for energy as,

E = x * hc/λ …… (i)

Where h = Planck’s constant = 6.626 * 10⁻³⁴Js

c = speed of light in vacuum = 3 * 10⁸ m/s

λ = wavelength of electromagnetic radiation is given as = 100 nm = 100 * 10⁻⁹ m

Substituting the values in eq. (i), we get

[66.26 * 60/100] = x * [6.626 * 10⁻³⁴ * 3 * 10⁸] / [100 * 10⁻⁹]

⇒ x =  [66.26 * 60/100 * 100 * 10⁻⁹] / [6.626 * 10⁻³⁴ * 3 * 10⁸]

⇒ x = [(60*10)/3] * [10⁻⁹ * 10⁻⁸ * 10³⁴]

⇒ x = 200 * 10¹⁷ = 2 * 10¹⁹ ← no.of quanta emitted

Thus, the no. of quanta emitted by the bulb per second is 2 * 10¹⁹.