Question

Calculate the speed (in m/s) of an electron and a proton with a kinetic energy of 1.90 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 3.19 ✕ 102 K ideal gas particle. (Recall from Topic 10 that 1 2 mv2 = 3 2 kBT.) eV

Answer 1

The kinetic energy of the non-relativistic particle is
  
  
a)
So, for the electron, with given values,
   
we get the speed of the electron
   
  
b)
For proton, with given values,
    
we get the speed of the proton
   
  
c)
Translational energy at temperature T is
   
So, for the given values,
  
we get the translational energy in the Joule unit
   

In the eV unit this energy is given by