Question

Suppose a beam of 5.10 eV protons strikes a potential energy barrier of height 5.80 eV and thickness 0.810 nm, at a rate equivalent to a current of 980 A. (a) How many years would you have to wait (on average) for one proton to be transmitted through the barrier? (b) How long would you have to wait if the beam consisted of electrons rather than protons?

Answer 1

Given the energy of the proton
  
And
  
And the thickness of the barrier is
  
So, the transmission coefficient is given by
  
So, putting the values, and putting the mass of the proton m = 1.6725 * 10^{-27} kg. So, by putting the given values, we get
  
Now, the current is given by
   
So, the incident number current is
  
So, the transmitted number current
  
So, the required time for a proton to transmit through the barrier is
  

b)

Transmitted coefficient for an electron in the above case is given by (just replacing the mass by m =9.11*10^{-31} kg)
we get

And so, the transmitted number current for electron is

So,
the required time for an electron to transmit through the barrier is