Question

Calculate the speed (in m/s) of an electron and a proton with a kinetic energy of 1.25 electron volt (eV). (The electron and proton masses are me = 9.11 ✕ 10−31 kg and mp = 1.67 ✕ 10−27 kg. Boltzmann's constant is kB = 1.38 ✕ 10−23 J/K.)

Answer 1

Answer:

6.63 x 10⁵ m/s

0.16 x 10⁵ m/s

Explanation:

$m_{e}$ = mass of the electron = 9.11 x 10⁻³¹ kg

$m_{p}$ = mass of the proton = 1.67 x 10⁻²⁷ kg

$v_{e}$ = speed of electron

$v_{p}$ = speed of proton

$K_{e}$ = Kinetic energy of electron = 1.25 eV = 1.25 x 1.6 x 10⁻¹⁹ J

Kinetic energy of electron is given as

$K_{e}=(0.5)m_{e}v_{e}^{2}$

$1.25\times 1.6\times10^{-19} = (0.5)(9.11\times 10^{-31})v_{e}^{2}$

$v_{e}$ = 6.63 x 10⁵ m/s

Kinetic energy of proton is given as

$K_{p}=(0.5)m_{p}v_{p}^{2}$

$1.25\times 1.6\times 10^{-19} =(0.5)(1.67\times 10^{-27})v_{p}^{2}$

$v_{p}$ = 0.155 x 10⁵ m/s