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  4. The total energy of an electron in the first excited state of the hydrogen atom is about -3.4 eV . The potential energy of the electron in this state is

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Q. The total energy of an electron in the first excited state of the hydrogen atom is about $-3.4\,eV$ . The potential energy of the electron in this state is

NTA AbhyasNTA Abhyas 2022Atoms

Solution:

The kinetic energy of an electron, $\left(K E\right)=\frac{K Z e^{2}}{2 r}$
The potential energy of an electron, $\left(\right.PE\left.\right)=\frac{- K Z e^{2}}{r}\Rightarrow PE=-2KE$
In this calculation, the electric potential and potential energy are zero at infinity.
Total energy $=PE+KE=-2KE+KE=-KE$
$PE$ of an electron in this first excited state
$=-2KE=-2\left(\right.3.4\left.\right)=-6.8\,eV$