First slide

Photoelectric effect and study of photoelectric effect

Question

A beam of electromagnetic radiation of intensity $6.4 \times 10^{- 5}$ $W / c m^{2}$ is comprised of wavelength, $λ = 310$ nm. It falls normally on a metal(work function $φ = 2 e V$ ) of surface area 1 $c m^{2}$ . If one in $10^{3}$ photons ejects an electron, total number of electrons ejected in 1s is $10^{x}$ (hc = 1240 eVnm, 1eV = $1.6 \times 10^{- 19}$ J) , then x is _____

Moderate

Solution

Power incident $P = I \times A$
n = no. of photons incident / second
$∴ n E_{p h} = I A \Rightarrow n = \frac{I A}{E_{p h}}$
$\Rightarrow n = \frac{I A}{(\frac{h c}{λ})} = \frac{6.4 \times 10^{- 5} \times 1}{\frac{1240}{310} \times 1.6 \times 10^{- 19}}$
$\Rightarrow n = 10^{+ 14}$ photons per second
Since efficiency $= 10^{- 3}$
No. of electrons emitted $= 10^{+ 11}$ per second.
$\Rightarrow x = 11$ .

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