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In mathematical representation of bohr's energy, E n = KE + PE E n = 1/2 mv 2 + (– KZe 2 / r n ) here, can you please explain me how can we arrive at the above mentioned value of potential energy??

In mathematical representation of bohr's energy,

En = KE + PE

En = 1/2 mv2 + (– KZe2 / rn) 

here, can you please explain me how can we arrive at the above mentioned value of potential energy??

Grade:11

1 Answers

Eshan
askIITians Faculty 2095 Points
5 years ago
Dear student,

This is the potential energy of system of an electron and nucleus of the atom with sepraration ofr_nbetween them. Charge of the electron iseand that of nucleus of atomic numberZisZe.

Hence the force acting on the electron at distanceris-\dfrac{k(Ze)(e)}{r^2}.
Hence the work done in bring charge from infinity to its orbit = Potential energy of the sytsem=-\int_\infty^{r_n}(-\dfrac{kZe^2}{r^2})dr
=-\dfrac{kZe^2}{r_n}

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