An electron at rest is released far away from a proton, towardwhich it moves. (a) Show that the de...

Question

An electron at rest is released far away from a proton, toward
which it moves. (a) Show that the de Broglie wavelength of the
electron is proportional to r, where ris the distance of the
electron from the proton. (b) Find the wavelength of the electron when it is a0 from the proton. How does this compare
with the wavelength of an electron in a ground-state Bohr orbit? (c) In order for the electron to be captured by the proton
to form a ground-state hydrogen atom, energy must be lost by
the system. How much energy?

Robert · Accepted Answer

a. It is given that the electron is at rest and is released far from a distance to the proton towards 
which it moves  
So in this process total energy if the system of electron and proton is conserved that is  
E+K+U=0 
Where E is the total energy 
K is the kinetic energy 
U is the potential energy 
Since total energy of system is 0 so 
U=-K ---(!) 
Now we know  K=

Where p is the momentum of electron and m is its mass.

An electron at rest is released far away from a proton, toward which it moves. ( a ) Show that the de Broglie wavelength of the electron is proportional to r , where r is the distance of the...

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