A researcher is using the following experimental setup to determine the work function of an unknown metal used as the cathode They measure the following stopping potentials for the given wavelengths o

The stopping potential V is related to the frequency f of the incident light and the work function W of the metal by:

V = (h/e) f - W

where h is Planck's constant and e is the elementary charge. We can rearrange this equation to solve for W:

W = (h/e) f - V

Using the given wavelengths, we can calculate the corresponding frequencies:

f = c/λ

where c is the speed of light. Substituting the values given, we get:

f(180 nm) = 2.998 x 10^8 m/s / (180 x 10^-9 m) = 1.665 x 10^15 Hz f(210 nm) = 2.998 x 10^8 m/s / (210 x 10^-9 m) = 1.427 x 10^15 Hz f(240 nm) = 2.998 x 10^8 m/s / (240 x 10^-9 m) = 1.249 x 10^15 Hz

Substituting these values and the given stopping potentials into the equation for W, we get:

W(180 nm) = (6.626 x 10^-34 J s / 1.602 x 10^-19 C) x 1.665 x 10^15 Hz - 2.59 V = 4.33 eV W(210 nm) = (6.626 x 10^-34 J s / 1.602 x 10^-19 C) x 1.427 x 10^15 Hz - 1.60 V = 4.43 eV W(240 nm) = (6.626 x 10^-34 J s / 1.602 x 10^-19 C) x 1.249 x 10^15 Hz - 0.87 V = 4.66 eV

Taking the average of these values (to account for experimental error), we get:

W = (4.33 + 4.43 + 4.66) / 3 = 4.47 eV

Therefore, the work function of the metal is 4.47 eV