Question

The angular speed of the electron in nth orbit of Bohr hydrogen
atom is
(a) Directly proportional to n
(b) Inversely proportional of √n
(c) Inversely proportional to n²
(d) Inversely proportional to n³

Answer 1

The angular speed of an electron in the nth orbit is inversely proportional to the square of n.

1)Orbital speed is inversely proportional to n^2.

2)This is due to the fact that greater the value of n,the larger is the electron orbit.

3)Electrons in the larger orbits have greater potential energy but low kinetic energy and hence velocity.

Answer 2

The angular speed of the electron in nth orbit of Bohr hydrogen is inversely proportional to n³

Explanation:

Form the Bohr's theory,

Speed of an electron in nth orbit, $v \propto n$ .........(1)

Radius of the orbit, $r \propto n^{2}$...........(2)

Time period, $T = \frac{2\pi r}{v}$

$2\pi$ is a constant. Hence $T \propto \frac{r}{v}$............(3)

From (1), (2) and (3)

$T \propto \frac{n^2}{\frac{1}{n} }$

$\Rightarrow T \propto n^{3}$

Angular speed, $\omega =\frac{2\pi}{T}$

  $\Rightarrow \omega \propto \frac{1}{n^3}$

Hence, The angular speed of the electron in nth orbit of Bohr hydrogen is inversely proportional to n³

Therefore the correct option is (d)