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  4. An α particle and a carbon 12 atom has same kinetic energy K. The ratio of their de-Broglie wavelength (λa: λC 12) is :

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Q. An $\alpha$ particle and a carbon $12$ atom has same kinetic energy $K$. The ratio of their de-Broglie wavelength $\left(\lambda_{a}: \lambda_{C 12}\right)$ is :

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Solution:

$k=\frac{P^{2}}{2 m} \Rightarrow P \alpha \sqrt{m}$
Now $\lambda=\frac{h}{p}$
So, $\lambda \alpha \frac{1}{p} \Rightarrow \lambda \alpha \frac{1}{\sqrt{m}}$
$\frac{\lambda_{\alpha}}{\lambda_{C 12}}=\frac{\sqrt{3}}{1}$