Dual Nature of Radiation and Matter - Result Question 3
3. A proton and an $\alpha$-particle are accelerated from rest to the same energy. The de Broglie wavelengths $\lambda_p$ and $\lambda_a$ are in the ratio,
[NEET Odisha 2019]
(a) $4: 1$
(b) $2: 1$
(c) $1: 1$
(d) $\sqrt{2}: 1$
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Answer:
Correct Answer: 3. (b)
Solution:
(b) As $\lambda=\frac{h}{p}=\frac{h}{\sqrt{2 m K}}$
$\therefore \lambda \propto \frac{1}{\sqrt{m}}$
(Kinetic energies are same)
$ \frac{\lambda_p}{\lambda _{\alpha}}=\sqrt{\frac{m _{\alpha}}{m_p}} \sqrt{\sqrt{7}} $
$ \therefore \quad \frac{\lambda_p}{\lambda _{\alpha}}=\frac{2}{1} $
