Question

In Bohr's model of the hydrogen atom, let $R,V,T,$ and $E$ represent the radius of the orbit, speed of the electron, time period of the revolution of electron and the total energy of the electron, respectively. The quantities proportional to the quantum number $n$ are

• A. $VR$
• B. $RE$
• C. $\frac{T}{R}$
• D. $\frac{V}{E}$

Answer 1

Answer: (A), (C), (D)

The correct options are
A $VR$
C $\frac{T}{R}$
D $\frac{V}{E}$

Radius of n th orbit : $R\propto \frac{n^2}{Z}=n^2...\left(1\right)$ (for hydrogen atom $Z=1$)

Velocity, $V\propto Z/n=1/n...\left(2\right)$ ;

Time period $T=\frac{2\pi R}{V}$

Using (1) and (2), $T\propto n^3...\left(3\right)$

Total energy , $E\propto Z^2/n^2=1/n^2.....\left(4\right)$

Using (1) and (2) $VR\propto n$

Using (1) and (4) $RE=1$

Using (1) and (3) $T/R\propto n$

Using (2) and (4) $V/E\propto n$