JEE Main · 2021 · 25 Jul 2021 · Shift 1 · Atomic Structure

A source of monochromatic radiation of wavelength 400 nm provides 1000 J of energy in 10 seconds. When this radiation falls on the surface of sodium,

x \times 1 0^{20}

electrons are ejected per second. Assume that wavelength 400 nm is sufficient for ejection of electron from the surface of sodium metal. The value of

x

is ______ (Nearest integer)
(

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

)

Answer: 2

Solution

Each photon of the radiation carries

E = \frac{h c}{λ} = \frac{6.626 \times 1 0 ^{- 34} \times 3 \times 1 0 ^{8}}{400 \times 1 0 ^{- 9}} = 4.97 \times 1 0^{- 19} J

The source delivers

\frac{1000}{10} = 100 J s^{- 1}

, so the number of photons striking the metal each second is

\frac{100}{4.97 \times 1 0 ^{- 19}} = 2.01 \times 1 0^{20}

. Since the wavelength is short enough to eject an electron, each photon releases one electron, giving

2.01 \times 1 0^{20}

electrons per second. To the nearest integer the value asked for is

2

JEE Main · 2021 · 25 Jul 2021 · Shift 1 · Integer answer