Question

1. The total energy of a moving electron is 0.850 MeV. What is the speed of the electron in terms of c?

A 0.306 c

B. 0.854 c

C. 0.933 c

D. 0.799 c

2. Calculate the kinetic energy of an electron moving at 0.834 c. Express your answer in keV.

A. 420 keV

B. 350 keV

C. 540 keV

D. 480 keV

Answer 1

1.

given data

energy= 0.850 MeV

1Mev = 1.6x10^-13 Joules

energy= 0.850*1.602*10^-13 J =1.3617*10^-13 J

From relativity

The total energy formula is;

E = Mc^2
E= Mo*c^2/SqRt[1-v^2/c^2]

E = m_0 c²/√(1–v²/c²)
√(1–v²/c²) = m_0 c²/E
1–v²/c² = (m_0 c² / E)²
v²/c² = 1 – (m_0 c² / E)²
v/c = √(1 – (m_0 c² / E)²)

v/c =  √ (1-((9.1*10^-31*3*10^8*3*10^8)/(1.3617*10^-13))^2)

v=0.799c

2. v=0.834c

KE = m0 c^2 (1/sqrt(1-v^2/c^)-1)

KE = 9.1*10^-31*3*10^8*3*10^8*((1/sqrt(1-0.834^2))-1) =6.653*10^-14 J

1J = 6.242*10^18 eV = 6.242*10^15 KeV

KE = 6.653*10^-14* 6.242*10^15 KeV =420 keV