Question

find the phase velocity and group velocity of particle moving with velocity of 0.9 c​

Answer 1

Answer:

3

Explanation:

Answer 2

$v_g=0.9c=2.7\times 10^8\ m.s^{-1}$ is the group velocity

$v_f=3.33\times 10^8\ m.s^{-1}$ is the phase velocity

Explanation:

• Let the mass of particle be, $m_0$

• velocity of particle is its group velocity, $v_g=0.9c=2.7\times 10^8\ m.s^{-1}$

Since the velocity of the particle is comparable to the velocity of light, we need its relativistic mass:

$m=\frac{m_0}{\sqrt{1-(\frac{v_g}{c})^2 } }$

Now according to Einstein's mass energy equivalence:

$E=m.c^2$ .....................................(1)

and the momentum of this relativistic mass:

$p=m.v_g$ .......................................(2)

Now the phase velocity is given as:

$v_f=\frac{E}{p}$

$v_f=\frac{m.c^2}{m.v_g}$

$v_f=\frac{c^2}{v_g}$

putting respective values in above eq.

$v_f=\frac{9\times 10^{16}}{2.7\times 10^8}$

$v_f=3.33\times 10^8\ m.s^{-1}$

TOPIC: theory of relativity

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