Question

Calculate the speed (in m/s) of an electron and a proton with a kinetic energy of 1.70 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.)

(a) an electron m/s

(b) a proton m/s

(c) Calculate the average translational kinetic energy in eV of a 3.15 ✕ 102 K ideal gas particle. (Recall from Topic 10 that 1 2 mv2 = 3 2 kBT.)

___eV

Answer 1

Given:-

• Kinetic energy of electron and proton
• Mass of electron
• Mass of proton
• Boltzmann constant
• Temperature of ideal gas particle

Now we have the relation of kinetic energy (K) and speed of the particle and is given as,

(a) Speed of an electron in m/s :-

                 

An electron with kinetic energy of 1.70 eV has speed

(b) Speed of a proton in m/s :-

A proton with kinetic energy of 1.70 eV has speed

(c) Average translational kinetic energy at temperature T = 315 K is given as,

We know that kinetic energy is directly proportional to temperature of the gas for ideal gas.

         where,

                         K = Kinetic energy,   = Boltzmann constant and

                         T = Temperature = 315 K

is the required average translational kinetic energy.