Question

The work function of a substance is $4.0eV$ . The longest wavelength of light that can cause photoelectron emission from this substance is approximate.
(A) $540nm$
(B) $400nm$
(C) $310nm$
(D) $220nm$

Answer 1

Energy carried by a single photon is called photon energy. The electromagnetic energy of the photons is directly proportional to the speed of light in a vacuum and is inversely proportional to the wavelength. The formula of the Photon energy in terms of wavelength is needed here.

Complete answer:
The light wavelength is inversely proportional to the photon energy. 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. Usually, when the photon's energy equals the substance's work function this will happen.
We have,
${E_\gamma } = 4.0ev$
${E_\gamma }$ is called photon energy.
The photon energy can be written as,
${E_\gamma } = \dfrac{{hc}}{\lambda }$
Here,
$h$ is planck's constant
$c$ is the speed of the light
$\lambda$ is the wavelength of the light
Use, $hc = 1240eV$
Then,
$4eV = \dfrac{{1240eV.nm}}{\lambda }$
Rearranging the above equation we get as follows,
$\lambda = \dfrac{{1240eVnm}}{{4eV}}$
After simplification,
$\lambda = 310nm$
Finally, the correct answer is an option (C).

Note:
-Any unit of energy can help to express the photon energy
-The commonly used to denote photon energy are the electron volt (eV) and the joule
$6.24 \times 10^{18}$ eV, is equal to one joule.
-The larger units help to refer to the photon energy with high frequency and high energy, they are like gamma rays as objects to smaller energy photons, like that they are present in the radio frequency region.