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

The Correct Option is C

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

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

Answer 2

Using Bohr’s postulate: angular momentum \( L = mvr = \frac{nh}{2\pi} \). Therefore: \[ m r \omega^2 = \frac{nh}{2\pi} \] \[ \Rightarrow r \propto \sqrt{n} \]