Question

In the Bohr model of the hydrogen atom, let R, V and E represent the radius of the orbit, speed of the electron and the total energy of the electron respectively. Which of the following quantities are proportional to the quantum number n ?

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

Answer 1

Answer: (A), (C)

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

$WKT,R\propto n^2,v\propto \frac{1}{n}andE\propto \frac{1}{n^2}$
$\Rightarrow VR\propto n$
$\Rightarrow RE=constant$
$\Rightarrow \frac{V}{E}\propto n$
$\Rightarrow \frac{R}{E}\propto n^4$