Question

The mean momentum of a nucleon inside a nucleus with mass number $A$ varies as

• A. $A^3$
• B. $A^{-\frac{2}{3}}$
• C. $A^{-\frac{1}{3}}$
• D. $A^{\frac{1}{3}}$
• E. $A^{\frac{2}{3}}$

Answer 1

Answer: (C)

From the Heisenberg uncertainty principle, $\Delta p\ge \frac{h}{4\pi \Delta r}$ $p\lambda =constant.$
$p\propto \frac{1}{\lambda }\approx \frac{1}{r}\approx \frac{1}{A^{\frac{1}{3}}}$