Question

In the Bohr model of the hydrogen atom.

• A. The radius of the $n^{th}$ orbit is proportional to $n^2$
• B. The total energy of the electron in the $n^{th}$ orbit is inversely proportional to ${}^{\prime }{n}^{\prime }$
• C. The angular momentum of the electron in an orbit is an integral multiple of $h/2\pi$
• D. The magnitude of the potential energy of the electron in any orbit is greater than its kinetic energy

Answer 1

Answer: (A), (D)

The correct options are
A The radius of the $n^{th}$ orbit is proportional to $n^2$
D The magnitude of the potential energy of the electron in any orbit is greater than its kinetic energy

Radius of Bohr's orbit of hydrogen atom is given by

$r=\frac{n^2{h}^2}{4{\pi }^{2}mKz{e}^2}$ or

$r=\left(0.59\mathring{A}\right)\frac{n^2}{z}$

So from expression we found $r\propto n^2$

And according to Bohr's theory

Angular momentum of elctron in an orbit will be Integral multiple of $\left(h/2\pi \right)$

Magnitude of potential energy is twice of kinetic energy of electron in an orbit

$|P.E|=2|K.E|$

$K.E=\left(13.6ev\right)\frac{\left(z^2\right)}{\left(n^2\right)}$