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

1 Answer
Carlos S.
Jan 24, 2018

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.

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