For photo-electric effect with incident photon wavelength $\lambda$, the stopping potential is $\mathrm{V}_{0}$. Identify the correct variation(s) of $\mathrm{V}_{0}$ with $\lambda$ and $1 / \lambda$.

(A) (see structure); (C) (see structure)

JEE Advanced · 2015 · 24 May 2015 · Paper 1 · Modern Physics

For photo-electric effect with incident photon wavelength

λ

, the stopping potential is

V_{0}

. Identify the correct variation(s) of

V_{0}

with

λ

and

1/ λ

Answer: (A), (C)

From Einstein's photoelectric equation:

\frac{h c}{λ} = e V_{0} + ϕ

V_{0} = \frac{h c}{e} \cdot \frac{1}{λ} - \frac{ϕ}{e}

This shows:

$V_{0}$ vs $1/ λ$ is a straight line with positive slope $h c / e$ and negative y-intercept $- ϕ / e$ (option A is correct)
$V_{0}$ vs $λ$ is a rectangular hyperbola that approaches zero as $λ \to \infty$ and has a vertical asymptote at $λ_{0} = h c / ϕ$ (threshold wavelength). For $λ > λ_{0}$ , $V_{0} = 0$ (option C is correct)

Options B and D show incorrect functional forms.

JEE Advanced · 2015 · 24 May 2015 · Paper 1 · One or more correct options