a Calculate its kinetic energy in joules at 580 of the speed

(a) Calculate its kinetic energy in joules at 5.80% of the speed of light.
J

(b) What is this in electron volts?
eV

(c) What voltage would be needed to obtain this energy?
V

Solution

a)

at v = 0.058 c

kinetic energy = m0 * c^2/sqrt(1 - (v/c)^2) - m0 * c^2

kinetic energy = 6.64 *10^-27 * (3 *10^8)^2/sqrt(1 - 0.058^2) - 6.64 *10^-27 * (3 *10^8)^2

kinetic energy = 1.01 *10^-12 J

the kinetic energy of Helium atom is 1.01 *10^-12 J

b)

converting to eV

kientic energy = 1.01 *10^-12/(1.602 *10^-19)

kientic energy = 6.304 *10^6 eV

c)

let the voltage nedeed is V

2 * e * V = kinetic energy

2 * V * e = 6.304 *10^6 eV

V = 3.15 *10^6 V

the potential needed is 3.15 *10^6 V