An -particle and a proton are accelerated from rest by a potential difference of 100 V. After this, their de Broglie wavelengths are and , respectively. The ratio to the nearest integer, is [2010]

Question

An $α$ -particle and a proton are accelerated from rest by a potential difference of 100 V. After this, their de Broglie wavelengths are $λ_{α}$ and $λ_{p}$ , respectively. The ratio $\frac{λ_{p}}{λ_{α}},$ to the nearest integer, is [2010]

Smart Achievers · Accepted Answer

(3)

We know that, $λ_{α}$ or, $λ \propto \frac{1}{\sqrt{q m}}$

$∴$ $\frac{λ_{p}}{λ_{α}} = \sqrt{\frac{m_{α} q_{α}}{m_{p} q_{p}}} = \sqrt{\frac{4}{1} \times \frac{2}{1}} = \sqrt{8} \approx 3$

Solution

Q.
An $α$ -particle and a proton are accelerated from rest by a potential difference of 100 V. After this, their de Broglie wavelengths are $λ_{α}$ and $λ_{p}$ , respectively. The ratio $\frac{λ_{p}}{λ_{α}},$ to the nearest integer, is [2010]

Ans.
(3)

We know that, $λ = \frac{h}{\sqrt{2 m q V}}$ or, $λ \propto \frac{1}{\sqrt{q m}}$

$∴$ $\frac{λ_{p}}{λ_{α}} = \sqrt{\frac{m_{α} q_{α}}{m_{p} q_{p}}} = \sqrt{\frac{4}{1} \times \frac{2}{1}} = \sqrt{8} \approx 3$

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Solution

Q. An α-particle and a proton are accelerated from rest by a potential difference of 100 V. After this, their de Broglie wavelengths are λα and λp, respectively. The ratio λpλα, to the nearest integer, is [2010]

Ans. (3) We know that, λ=h2mqV or, λ∝1qm ∴ λpλα=mαqαmpqp=41×21=8≈3

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Q.
An $α$ -particle and a proton are accelerated from rest by a potential difference of 100 V. After this, their de Broglie wavelengths are $λ_{α}$ and $λ_{p}$ , respectively. The ratio $\frac{λ_{p}}{λ_{α}},$ to the nearest integer, is [2010]

Ans.
(3)

We know that, $λ = \frac{h}{\sqrt{2 m q V}}$ or, $λ \propto \frac{1}{\sqrt{q m}}$

$∴$ $\frac{λ_{p}}{λ_{α}} = \sqrt{\frac{m_{α} q_{α}}{m_{p} q_{p}}} = \sqrt{\frac{4}{1} \times \frac{2}{1}} = \sqrt{8} \approx 3$