For a rectangular metal surface with dimensions 5 cm by 3 cm, the threshold wavelength for the photoelectric emission of electrons is 246.0 nm.

(a) Calculate the work function of the metal surface.

So I planned to use: hf - workfunction = eV

Then I replace f with c/lambda, since c = (f)(lambda)

So I have:
(4.135*10^-15 eV*s)(3.00*10^8 m/s)/246.0*10^-9 m - workfunction = eV

Clearly I am missing something or a lot of things, so how am I supposed to solve for the workfunction using the given information about the dimensions of the metal surface? Are the dimensions even important and if so, how?

Threshold energy=e*c/lamda

dimensions are a red herring here.

To solve for the work function of the metal surface, you need to use the equation you've mentioned correctly. Here's how you can approach it step by step:

1. The equation hf - work function = eV relates the energy of a photon (hf), the work function of the metal surface (work function), and the kinetic energy of the emitted electron (eV).

2. In this case, you are given the threshold wavelength for the photoelectric emission of electrons (246.0 nm). Recall that the threshold wavelength corresponds to the minimum wavelength of light that can cause the photoelectric effect.

3. Firstly, convert the threshold wavelength from nanometers (nm) to meters (m):
Threshold wavelength = 246.0 nm = 246.0 x 10^-9 m

4. Now, you can calculate the frequency (f) of the photon using the speed of light (c) and the threshold wavelength (lambda):
f = c / lambda = (3.00 x 10^8 m/s) / (246.0 x 10^-9 m)

5. Next, calculate the energy of the photon (hf) using Planck's constant (h) and the frequency (f):
hf = h x f = (4.135 x 10^-15 eV s) x [(3.00 x 10^8 m/s) / (246.0 x 10^-9 m)]

6. Since the energy is given in electron volts (eV), convert the energy from joules (J) to electron volts (eV):
1 eV = 1.602 x 10^-19 J
Energy in eV = (hf) / (1.602 x 10^-19 J/eV)

7. Finally, you can plug in the known values into the equation to solve for the work function:
Work function = (hf) - (eV)

By following these steps and plugging in the appropriate values, you should be able to find the work function of the metal surface.