Consider a thin target (10 –2 m square, 10 -3 m thickness) of sodium, which produces a photocurrent of 100μA when a light of intensity 100W/m 2 (λ = 660nm) falls on it. Find the probability that a photoelectron is produced when a photons strikes a sodium atom. [Take density of Na = 0.97 kg/m 3 ].

Question

Philoid · Accepted Answer

Area of cross-section of the target = 10^-2 x 10^-2 m² = 10^-4 m²

Thickness = 10^-3 m

Volume = Area x thickness = 10^-7 m³

Density of Sodium = 0.97kg/m³

Mass of the Sodium target (W) = Density x Volume = 9.7 x 10^-8 kg/m³

Mol. Mass of Sodium (M) = 23g

Number of atoms of Sodium will be given by

Let ‘n’ be the number of photons emitted in 1 second

Energy emitted in 1 second is equal to power since power is energy/time

Also, we know, h (Plank’s Constant), c (speed of light in vacuum), and (wavelength of incident radiation) can determine a photon’s energy.

Total energy emitted = 100J per second

Let the number of photoelectrons produced to supply a 100μA current be ‘N’

We know that current (I) is given by charge (q) per unit time (t)

Here, q = N x e, where ‘e’ is the charge on electron.

Let the probability of a photoelectron being produced when a photon strikes a sodium atom be denoted by P(E)

Then number of photoelectrons emitted per atom, per photon will be

So,

Consider a thin target (10–2m square, 10-3 m thickness) of sodium, which produces a photocurrent of 100μA when a light of intensity 100W/m2 (λ = 660nm) falls on it. Find the probability that a photoelectron is produced when a photons strikes a sodium atom. [Take density of Na = 0.97 kg/m3].

Consider a thin target (10^–2m square, 10^-3 m thickness) of sodium, which produces a photocurrent of 100μA when a light of intensity 100W/m² (λ = 660nm) falls on it. Find the probability that a photoelectron is produced when a photons strikes a sodium atom. [Take density of Na = 0.97 kg/m³].