On the basis of Heisenberg's uncertainty principle, show that ele… - Vidyadip

Question

On the basis of Heisenberg's uncertainty principle, show that electron cannot exist within the atomic nucleus.
(Nuclear radius $=10^{-15} \mathrm{~m}, \mathrm{~h}=6.626 \times 10^{-34} \mathrm{~J} \mathrm{~s}$ ).

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Answer

$\Delta\text{x},\Delta\text{v}=\frac{\text{h}}{4\text{m}\pi}$ [Heisenberg's uncertainty principle]
Uncertainty in velocity,
$\Delta\text{v}=\frac{6.626\times10^{-34}\text{Js}}{4\times9.1\times10^{-31}\text{kg}\times3.142\times10^{-15}\text{m}}$
$=5.7\times10^{10}\text{ms}^{-1}$
Since this value is more than the velocity of light which is impossible, therefore, electron cannot exist within the nucleus.

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