Special Relativity - Relativistic Energy

What is the speed of a particle having a momentum of 5 MeV/c and a total relativistic energy of 10 MeV?

A. c
B. 0.75 c
C. 1/√3 c
D. ½ c
E.  ¼ c

(GR9677 #38)

Solution:

p = γm₀v
E = γm₀c²

p/E = v/c²
v = pc²/E = (5 MeV/c) c²/10 MeV = ½ c

Answer: D

Special Relativity - Momentum

A monoenergetic beam consists of unstable particles with total energies 100 times their rest energy. If the particles have rest mass m, their momentum is most nearly 

A. mc
B. 10 mc
C. 70 mc
D. 100 mc
E. 10⁴ mc

(GR9277 #70)

Solution:

E = γE₀ = 100E₀ → γ = 100
p = γm₀c = 100 mc

Answer: D

Special Relativity - Relativistic Energy

A free electron (rest mass m_e = 0.5 MeV/c²) has a total energy of 1.5 MeV. Its momentum p in units of MeV/c is about

A. 0.86
B. 1.0
C. 1.4
D. 1.5
E. 2.0

(GR9277 #85)

Solution:

E² = p²c² + m₀²c⁴

1.5² = p²c² + (0.5/c²)²c⁴

 p²c² = 1.5² − 0.5² = 2

p = ^√2/_c ≈ ^1.4/_c

Answer: C

Special Relativity - Relativistic Momentum

If the total energy of a particle of mass m is equal to twice its rest energy, then the magnitude of the particle’s relativistic momentum is

A. mc/2
B. mc/√2
C. mc
D. √3mc
E. 2mc

(GR0177 #32)

Solution:

Rest Energy: E₀ = m₀c²

Relativistic Energy:  E² = p²c² + m₀²c⁴

Given: m₀ = m and E = 2E₀

p²c² + m²c⁴ = 4E₀² = 4m²c⁴
p² = 3m²c²
p = √3mc

Answer: D