Question

Part A

Find the speed of an electron with a kinetic energy 2.00×10⁻¹³ J .

Express your answer using two significant figures.

Part B

What's the speed of a proton with the same kinetic energy?

Express your answer using two significant figures.

Answer 1

Part A )

m_e = mass of electron = 9.1 x 10^-31 kg

KE = kinetic energy of electron = 2 x 10^-13 J

v = speed of the electron = ?

Kinetic energy is given as

KE = m_e c² (1/(sqrt(1 - (v/c)²) - 1)

2 x 10^-13 = (9.1 x 10^-31 ) (3 x 10⁸)² (1/(sqrt(1 - (v/(3 x 10⁸))²) - 1)

v = 2.9 x 10⁸ m/s

part B)

m_p = mass of proton = 1.67 x 10^-27 kg

KE = kinetic energy of electron = 2 x 10^-13 J

v = speed of the electron = ?

Kinetic energy is given as

KE = m_p c² (1/(sqrt(1 - (v/c)²) - 1)

2 x 10^-13 = (1.67 x 10^-27) (3 x 10⁸)² (1/(sqrt(1 - (v/(3 x 10⁸))²) - 1)

v = 1.5 x 10⁷ m/s