Question

A typical atomic nucleus is about $5.0\times {10}^{-15}m$ in radius. Using the uncertainty principle, what should be the lower limit on momentum, that a particle must have if it is to be a part of a nucleus?

• A. $1.1\times {10}^{-20}kgm/s$
• B. $2.2\times {10}^{-20}kgm/s$
• C. $4.4\times {10}^{-20}kgm/s$
• D. No lower limit

Answer 1

The correct option is A $1.1\times {10}^{-20}kgm/s$

From Heisenberg's uncertainty principle,
$\Delta x.\Delta p\ge \frac{\hslash }{2}$
where $\Delta x$ is uncertainty in position and $\Delta p$ is uncertainty in momentum.
$\hslash =\frac{h}{2\pi }=1.05\times {10}^{-34}Js$

Here, $\Delta x=5\times {10}^{-5}m$
$\Rightarrow \Delta p\ge \frac{\hslash }{2\Delta x}$
$\Rightarrow \Delta p\ge \frac{1.05\times {10}^{-34}}{2\times 5\times {10}^{-5}}$
$\Rightarrow \Delta p\ge 1.1\times {10}^{-20}kgm/s$