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).

constant and the work function of a metal, using sodium as the test material. blogger-faq.html

How is Planck's constant determined using the photoelectric effect?

Planck's constant is determined by plotting a graph of stopping potential (V₀) against frequency (ν) of incident light. The slope of this straight-line graph equals h/e, so multiplying the slope by the electron charge (e) gives the value of Planck's constant.

What is the work function of a metal and how is it calculated?

The work function is the minimum energy needed to eject an electron from a metal's surface. It is calculated by multiplying the y-intercept (OC) of the stopping potential vs. frequency graph by the electron charge (e), using Einstein's photoelectric equation.

What is Einstein's photoelectric equation?

Einstein's photoelectric equation is ½mv₀² = h(ν − ν₀), which states that the maximum kinetic energy of an emitted electron equals the energy of the incident photon minus the work function of the metal. It relates the stopping potential, Planck's constant, and the frequency of incident light.