The total energy of an electron in an orbit of hydrogen atom is E. The potential energy of the electron in…

The total energy of an electron in an orbit of hydrogen atom is E. The potential energy of the electron in the same orbit is
  1. E
  2. $\frac{E}{2}$
  3. $2 \mathrm{E}$
  4. $3 \mathrm{E}$

Solution

Kinetic energy is given by $\mathrm{K} . \mathrm{E}=\frac{\mathrm{KZe}^2}{2 \mathrm{r}}$ Potential energy is given by $\text { P.E }=-\frac{K^2 e^2}{r}$ Total energy $=\mathrm{K} \cdot \mathrm{E}+\mathrm{P} . \mathrm{E}$ $\mathrm{E}=\frac{\mathrm{KZe}^2}{2 \mathrm{r}}-\frac{\mathrm{KZe}^2}{\mathrm{r}}$ $\begin{aligned} & E=\frac{-K Z e^2}{2 r} \\ & E=\frac{P \cdot E}{2} \\ & \Rightarrow P . E=2 E\end{aligned}$

Asked in: AP EAMCET 2023 (17 May Shift 1)

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