Question

Which of the following statements is true for hydrogen atom ?

• A. Angular moment $\propto \frac{1}{n}$
• B. Linear moment $\propto \frac{1}{n}$
• C. Radius $\propto \frac{1}{n}$
• D. Energy $\propto \frac{1}{n}$

Answer 1

Answer: (B)

Angular momentum
$L = mvr = \frac{nh}{2\pi}$
or $ mv = \frac{nh}{2\pi r}$
Now, $ r\propto n^2$
$\therefore mv = p \propto \frac{nh}{2\pi \times n^2}$
$\Rightarrow p \propto \frac{h}{2\pi n}$ or
$p \propto \frac{1}{n}$
Energy, $E \propto \frac{1}{n^2}$