Question

In the Bohr model of the hydrogen atom, the ratio of the kinetic energy to the total energy of the electron in a quantum state $n$ is:

• A. $-1$
• B. $+1$
• C. $\frac{1}{n}$
• D. $\frac{1}{n^2}$

Answer 1

The correct option is A $-1$

The total energy of electron of the hydrogen atom=

(-)The kinetic energy of that electron.

As we know,

$KE=\frac{kZ{e}^2}{2r}\to \left(1\right)PE=(-)\frac{kZ{e}^2}{r}\therefore TE=\frac{kZ{e}^2}{2r}+(-)\frac{kZ{e}^2}{r}=(-)\frac{kZ{e}^2}{r}\to \left(2\right)\therefore Fromequation\left(1\right)and\left(2\right),TE=(-)KE\frac{TE}{KE}=-1$