Which of the following statements regarding Bohr theory of hydrogen atom is not correct?

Which of the following statements regarding Bohr theory of hydrogen atom is not correct?
  1. Kinetic energy of an electron in an orbit is half of magnitude of its potential energy.
  2. Kinetic energy of an electron in an orbit is equal to the magnitude of its potential energy.
  3. Total energy of an electron is negative of its kinetic energy.
  4. Potential energy of an electron in an orbit is equal to \(-m v^{2}\).

Solution

Let an electron revolves with a constant speed $\mathrm{v}$ around the nucleus in a stationary orbit of radius $r$. The electrostatic force acting on the electron is balanced by the centrifugal force i.e. $F_c=F_e$
$\therefore \frac{m v^2}{r}=\frac{\mathrm{ke}^2}{\mathrm{r}^2} \quad$ where $\mathrm{k}=\frac{1}{4 \pi \epsilon_o}$
or $\mathrm{mv}^2=\frac{\mathrm{ke}^2}{\mathrm{r}}$ ... (1)
Thus kinetic energy of electron $\mathrm{K}=\frac{1}{2} \mathrm{mv}^2=\frac{\mathrm{ke}^2}{2 \mathrm{r}}$ ... (2)
Potential energy of electron $\mathrm{U}=\frac{-\mathrm{ke}^2}{\mathrm{r}}$
$\Rightarrow \mathrm{U}=-2 \mathrm{~K}$ (using (2)) ^

Asked in: JEE-TOPICTESTS-CHEMISTRY

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