Light of wavelength λ=4000 mathringA and intensity 100 W / m 2 is incident on a plate of threshold frequency 5.5 × 1014 Hz. Find the number of photons incident per m 2 per sec.

Question

Light of wavelength λ=4000 mathringA and intensity 100 W / m 2 is incident on a plate of threshold frequency 5.5 × 1014 Hz. Find the number of photons incident per m 2 per sec. (A)  1021  (B)  3.0× 1019  (C)  2.02× 1020  (D)  2.02× 1021

Tardigrade Admin · Accepted Answer

Let number of photons emitted per sec be n. Then, intensity =100 W / m2 ⇒ (n h c/λ)=100 ⇒ n=(100 × λ/h c) =(10 × 4000 × 10-10/6.6 × 10-34 × 3 × 108) =2.02 × 1020

Q. Light of wavelength $λ = 4000 \overset{˚}{A}$ and intensity $100 W / m^{2}$ is incident on a plate of threshold frequency $5.5 \times 1 0^{14} Hz$ . Find the number of photons incident per $m^{2}$ per sec.

$10^{21}$

$3.0 \times 10^{19}$

$2.02 \times 10^{20}$

$2.02 \times 10^{21}$

Let number of photons emitted per sec be $n$ . Then, intensity
$= 100 W / m^{2}$
$\Rightarrow \frac{nh c}{λ} = 100$
$\Rightarrow n = \frac{100 \times λ}{h c}$
$= \frac{10 \times 4000 \times 1 0 ^{- 10}}{6.6 \times 1 0 ^{- 34} \times 3 \times 1 0 ^{8}}$
$= 2.02 \times 1 0^{20}$

Q. Light of wavelength λ=4000A˚ and intensity 100W/m2 is incident on a plate of threshold frequency 5.5×1014Hz. Find the number of photons incident per m2 per sec.

1021

3.0×1019

2.02×1020

2.02×1021