1. The total energy of a moving electron is 0.850 MeV. What is the speed of the

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
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
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

Explanation / Answer

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

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