In the ground state of the hydrogen atom the electron has a

In the ground state of the hydrogen atom, the electron has a total energy of -13.6 eV. What are (a) its kinetic energy and (b) its potential energy if the electron is a distance 4.0a from the central nucleus? Here a is the Bohr radius.

Solution

for electron moving in circular path,

PE = - k q1 q2 / r

KE = k q2 q2 / 2r

where q1 is charge on nucleous and q2 = e and r is radius.

for r = a

total energy = PE + KE = k q e / a   - kq e / 2a = - k q e / 2a = - 13.6 eV

kq e / a = 27.2 eV

r = 4a

then

KE = k q e / 8a = 27.2/8 = 3.4 eV .........Ans (a)

(b) PE = - 2KE = - 6.8 eV