JEE Main · 2021 · 17 Mar 2021 · Shift 2 · Modern Physics

Two identical photo-cathodes receive the light of frequencies

f_{1}

and

f_{2}

respectively. If the velocities of the photo-electrons coming out are

v_{1}

and

v_{2}

respectively, then

Answer: (A)

Solution

Einstein's photoelectric equation applies to each cathode, and the two are identical, so the work function

ϕ

is the same for both:

\frac{1}{2} m v_{1}^{2} = h f_{1} - ϕ, \frac{1}{2} m v_{2}^{2} = h f_{2} - ϕ

Subtracting removes

ϕ

\frac{1}{2} m (v_{1}^{2} - v_{2}^{2}) = h (f_{1} - f_{2})

v_{1}^{2} - v_{2}^{2} = \frac{2 h}{m} (f_{1} - f_{2})

JEE Main · 2021 · 17 Mar 2021 · Shift 2 · Single correct option