In an experiment on the photo-electric effect Singly ionized helium is excited electronically to different energy levels. The light emitted by ionised helium is incident on photo-electric plate in a photocell. When helium is excited to fourth energy level, then the observed stopping potential of the photocell is found to be five times the stopping potential measured when the photoelectrons are produced by using light emitted by hydrogen atom, excited to the third energy level. Determine the work function of the material of the photo-electric plate.

Explanation

To solve the problem, we will follow these steps:

### Step 1: Determine the frequencies of emitted light for both helium and hydrogen.

For singly ionized helium (He+), when excited to the fourth energy level (n=4), the frequency of the emitted photon can be calculated using the formula:

\[
f_1 = Z^2 R_H \left( \frac{1}{1^2} - \frac{1}{4^2} \right)
...