Question

Assertion :An electron cannot exist in the nucleus. Reason: The de Broglie wavelength of an electron is much smaller than the diameter of the nucleus.

Read the above assertion and reason and choose the correct option regarding it.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is C Assertion is correct but Reason is incorrect

The diameter of the nucleus is in the range of $1.75fm(1.75\times {10}^{-15}m$) for hydrogen (the diameter of a single proton) to about $15fm$ for the heaviest atoms, such as uranium.

$\lambda =\frac{h}{P}=\frac{h}{mv}$

For an electron to exist in a nucleus, its de Broglie wavelength ($\lambda$) and the diameter of a nucleus ($d$) must have the following relation:

$\frac{\lambda }{2}<d$

Now putting value of de Broglie's wavelength,

$\frac{h}{mv}<2d$ $or$ $v>\frac{h}{2md}$

Putting value of $h$, $m$ (mass of electron), and the order of diameter of nucleus ($d$), we get $v>c$, where $c$ is the speed of light$=3\times {10}^8$, which is clearly not possible.

So, an electron cannot exist inside the nucleus.
So, Assertion is correct but Reason is incorrect