Physics, asked by gudimetlarishi1269, 9 months ago

Find the group velocity and phase velocity of a particle moving with velocity 0.9c

Answers

Answered by priyanshupal1212
0

g

=0.9c=2.7×10

8

m.s

−1

is the group velocity

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

f

=3.33×10

8

m.s

−1

is the phase velocity

Explanation:

Let the mass of particle be, m_0m

0

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

g

=0.9c=2.7×10

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 } }m=

1−(

c

v

g

)

2

m

0

Now according to Einstein's mass energy equivalence:

E=m.c^2E=m.c

2

.....................................(1)

and the momentum of this relativistic mass:

p=m.v_gp=m.v

g

.......................................(2)

Now the phase velocity is given as:

v_f=\frac{E}{p}v

f

=

p

E

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

f

=

m.v

g

m.c

2

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

f

=

v

g

c

2

putting respective values in above eq.

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

f

=

2.7×10

8

9×10

16

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

f

=3.33×10

8

m.s

−1

TOPIC: theory of relativity

.

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