Question

The potential energy of an electron is defined as U = $\frac 12$ mw2x2 and follows Bohr’s law. Radius of orbit as function of n depends on? (w is same constant)

• A. n2
• B. $\frac{1}{\sqrt{n}}$
• C. $\sqrt{n}$
• D. $n^\frac{2}{3}$

Answer 1

Answer: (C)

$\sqrt{n}$

Answer 2

$U = \frac{1}{2} mw^2x^2$
$mvx = \frac{nh}{2\pi}$
$\frac{mv^2}{x} = mw^2x$
$v = wx$
$x^2\propto n$
$x\propto\sqrt{n}$

So, the correct option is (C): $\sqrt{n}$