Question

The work function of a metal is 4.2 eV. If radiations of 2000${A^\circ }$ on the metal, then the kinetic energy of the fastest photoelectron is:
A.$1.6 \times {10^{ - 19}}J$
B.$16 \times {10^{ - 19}}J$
C.$3.2 \times {10^{ - 19}}J$
D.$6.4 \times {10^{ - 10}}J$

Answer 1

Hint:We have studied that; the energy of radiation is \[E = \dfrac{{hc}}{\lambda }\]. Radiation is the form of energy that moves through space from an object, the source, to a different object where then, it is absorbed. Radiation sources are basically collections of matter or devices that convert one form of energy into radiation. As in particular cases the energy which is to be converted is stored within the object itself.

Complete step by step answer:
As we know that \[E = \dfrac{{hc}}{\lambda }\],
where h is planck's constant & c is speed of light. \[E = \dfrac{{6.626 \times {{10}^{ - 34}} \times 3 \times {{10}^8}}}{{2000 \times {{10}^{ - 16}}}} = 9.939 \times {10^{ - 19}}J\]
\[E = \dfrac{{6.626 \times {{10}^{ - 34}} \times 3 \times {{10}^8}}}{{2000 \times {{10}^{ - 16}}}}\]
\[E = 9.939 \times {10^{ - 19}}J\]
The work function is
 \[\psi = 4.2{\text{ }}eV\]
\[\psi = {\text{ }}4.2 \times 1.602 \times {10^{ - 19}}J\]
\[\psi = 6.728 \times {10^{ - 19}}J\]
The kinetic energy of the fastest photon is
\[ = E - \psi \]
\[ = 9.939 \times {10^{ - 19}}J - 6.728 \times {10^{ - 19}}J = 3.2 \times {10^{ - 19}}J\]
Hence, the correct option is C.
You are probably familiar with these types of energy from a physics lecture that energy is the capacity to do work. You have a sense of what work is from regular life, its things that require effort. Energy and work have the same units. Kinetic energy which is the energy comes from the motion.

Note:
We must remember, in the process called photoemission, the electron gets absorbed in some material then the energy of one photon which acquires more energy than its work function of the material (the electron binding energy), is ejected. The number of excited electrons when emitted also changes because the probability that each electron which is impacting a photon results in an emitted electron is the function of the photon energy. The contents of photocathode are the combinations of chemical elements such as antimony, rubidium, and caesium which is specially chosen to provide a lower work function, so that when illumination takes place even by very low levels light, the photocathode could easily release electrons.