In an experiment on the photoelectric effect, an evecuated photocell with a pure metal cothode is used. Which graph best represents the variation of B, the minimum potential defference needed to prevent current from flowing, when x, the frequency of the incident light, is varied?

Options

A.
B.
C.
D.

Answer

B

Explanation

By Einstein's particle (photon) theory, the maximum kinetic energy `E_(max)` of the emitted electrons from the cathode is proportional to the frequency f of the light. This is expressed in the Einstein's photoelectric equation below
`E_(max)=hf-phi=hf-hf_0`
`=h(f-f_0)`..(i)
where h is the Planck's constant, `phi_0` is the work function of the metal and is related to the threshold frequency `f_0` by `phi_0=hf_0`. It is the minimum amount of work of energy necessary to take a free electron out of the metal against the attractive forces of surrounding positive ions.
At a particular negative potential difference V applied to the anode A, the current becomes zero. This is value of the negative potential difference which just stops the electrons with maximum energy from reaching A. V is called the stopping potential . Therefore,
`eV=E_(max)` ..(ii)
From Eqs. (i) and (ii), we have
`eV=E_(max)=h(f-f_0)`
`V=(h)/(e)(f-f_0)` or `y=(h)/(e)(x-x_0)`
The variation of V (or y) is thus a straight line of gradient `(h)/(e)`, when it is plotted against f(or x) at `f_0`. It is best represented in graph b.