Question

Write the postulates of Bohr's atomic model. What is the relationship between the radii of the $n$th and first bohr orbit of hydrogen atom?

Answer 1

1) An electron can revolve around the nucleus in certain fixed orbits of definite energy without emission of any radiant energy. Such orbits are called stationary orbits.

2) An electron can make a transition from a stationary state of higher energy $E_2$ to a state of lower energy $E_1$ and in doing so, it emits a single photon of frequency,

$v=\frac{E_2-E_1}{h}$ where $h$ is the plank constant.

Conversely, on absorbing an energy, $E_2-E_1$ when the electron is at energy $E_1$, the electron can take transition from $E_1$ to $E_2$.

3) Only those orbits are allowed for which the angular momentum of the electron is an integral multiple of $\frac{h}{2\pi }$.

thus $L=\frac{nh}{2\pi }$ where $n=1,2,\mathrm{3...}$

If radius of first bohr orbit is $r_1$ and radius of $n^{th}$ bohr orbit is $r_n$ then relation between them is given by,

$r_n=n^2{r}_1$