Determination of Planck’s Constant and Work Function of a Metal

Determination of Planck’s Constant and Work Function of a Metal

Using Einstein’s photoelectric equation, determine

(i) Planck’s constant and

(ii) Work function of a given material.

Solutions: 

According to Einstein’s photoelectric equation, we have

$\frac{1}{2}mv_0^2=h(\nu-\nu_0)$

Since, $\frac{1}{2}mv_0^2=eV_0$

where e is charge on an electron and $V_o$ is stopping potential,

$eV_0=h\nu-h\nu_0$

or

$V_0=\left(\frac{h}{e}\right)\nu-\frac{h\nu_0}{e}$

$V_0=\left(\frac{h}{e}\right)\nu-\frac{\phi_0}{e}...(i)$

Equation (i) can be compared with the equation of a straight line, 

y=mx+c

i.e. , where m  is the slope of the line and c is the intercept on y-axis. 

Thus, graph between $V_0$  and $\nu$  is a straight line having slope

$m=\frac{h}{e}$

and intercept (OC) =$-\frac{\phi_0}{e}$

slope of $V_0$ versus $\nu$ graph : 

$\frac{h}{e}=\tan\theta=\frac{\Delta V_0}{\Delta \nu}$

or

$h=e\times\tan\theta$

h= e × slope of $V_0$ versus $\nu$ graph ...(ii)

Using eqn. (ii), value of can be determined.

Intercept $(OC)=-\frac{\phi_0}{e}$

or

$|\phi_0|=(\text{intercept }OC)\times e...(iii)$

Using Eqn. (iii), work function of the given metal can be calculated.

R.A. Millikan was the first to measure the values of Planck’s constant and work function (for sodium).