Question

In a photoelectric experiment using a sodium surface, you find a stopping potential of 1.85 V for a wavelength of 300 nm and a stopping potential of 0.820 V for a wavelength of 400 nm. From these data find (a) a value for the Planck constant, (b) the work function Φ for sodium, and (c) the cutoff wavelength λ0 for sodium

Answer 1

The standard equation to use in this situation is \[E = h f - \phi \] Where E is the energy of the photon in Electron Volts (eV), h is the Planck constant, and phi is the work function for the material.

Since \[f = \frac{c}{\lambda}\] (c being the speed of light in m/s) then \[E = eV_0 = hf - \phi = \frac{h c}{\lambda} - \phi\]
Reworking the equation in terms of Volts, \[eV_0 = \frac{h c}{\lambda} - \phi\] becomes \[V_0 = \frac{h c}{e \lambda} - \frac{\phi}{e}\]where V_0 is your stopping potential, and e is the charge of an electron. With this equation, you can determine the work function and Planck constant with a little algebra.

I'd suggest using the last equation, plugging in your values for one wavelength, solving for one of the unknowns, and substituting it into the other equation.

Once you've done that, you should have the first two parts of the problem done.

The last part is asking at what wavelength does the work function equal the energy of the photon being emitted? In other words, when is the energy equal to zero? You can find this with the 4th equation.