Question

The momentum associated with photon is given by:
A. $h\nu $
B. $\dfrac{{h\nu }}{c}$
C. $hE$
D. $h\lambda $

Answer 1

Hint: To find out the relation between frequency and momentum of photon, the two relations that can be used are as follows:
$E = m{c^2}$
$E = h\nu $
Where $E$ = Energy of the photon
               $\nu $ = Frequency of photon
               $c$ = Velocity of light with which photon travel
By equating above two equations we can easily derive the momentum associated with the photon.

Complete step-by-step answer:
By energy mass relation of Einstein, every mass is converted into energy when it travel with the velocity of light by the equation
$E = m{c^2}$
Energy associated with each photon having frequency $\nu $ is given by,
$E = h\nu $
On equating both the equation we get
$m{c^2} = h\nu $
$mc = \dfrac{{h\nu }}{c} \cdot \cdot \cdot \cdot \cdot \cdot \left( 1 \right)$
Also momentum of photon given by
$p = mc \cdot \cdot \cdot \cdot \cdot \cdot \left( 2 \right)$
From (1) and (2) we get
$p = \dfrac{{h\nu }}{c}$
Hence the momentum associated with the photon given by $\dfrac{{h\nu }}{c}$.
Therefore the correct option is B.

Note: When we talk about photon energy then it means energy carried by a single photon. By the above relation we conclude that momentum of a photon is directly proportional to frequency of light. Hence on increasing the frequency of light, the momentum associated with a photon also increases.