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} $