Question

The work- function of a substance is 4.0 eV. The longest wavelength of light that can cause photoelectron emission from this substance is approximately ?: (1) 540 nm (2) 400 nm (3) 220 nm (4) 310 nm

Answer 1

310 nm.

Explanation:

Since the photon energy is inversely related to its correspondent light wavelength, the longest wavelength will be the one that leaves the photon on a threshold situation regarding its energy to free the photoelectron from the metal. Ideally, this would happen when the photon's energy equals the substance's work-function.

Then, we must have

`E_gamma = 4.0 eV` (where I used `E_gamma` to denote the photon's energy).

Moreover, the photon's energy can be written as

`E_gamma = (hc)/(lambda)`, where `h` is the Plank's constant, `c` is the speed of light in vaccum and `lambda` is the wavelength of light corresponding to this photon.

Using `hc = 1240 eVnm`, then:

`4 eV = (1240 eV *nm)/lambda`;

`lambda = (1240 cancel(eV) nm)/(4 cancel(eV))`;

then:

`lambda = 310 nm`.