Question

The proton is a particle with a positive charge equal in magnitude to that of an electron with a mass 1840× that of an electron (me = 9.1085 × 10-31 kg). Calculate the kinetic energy in electron volts, of a proton with a wavelength of 0.1 Å.

Answer 1

Given mass of proton   mp = 1840 * me

mp = 1840 * 9.1085 * 10^-31 kg

Charge of proton is 1.6 * 10^-19 C

wavelength lambda = 0.1 A = 0.1 * 10^-10 m

planck's constant h = 6.634 * 10^-34 J-s

According to deBroglie

lambda = h / (m * v)

0.1 * 10^-10 = (6.634 * 10^-34) / (1840 * 9.1085 * 10^-31 * v)

velocity of proton is v = 3.96 * 10^4 m/s

The kinetic energy is K = 1/2 * mp * v^2

K = 1/2 * (1840 * 9.1085 * 10^-31) * (3.96 * 10^4)^2

K = 1.31 * 10^-18 J

in eV the kinetic energy is

K = (1.31 * 10^-18) / (1.6 * 10^-19)

K = 8.19 eV