SATHEE: Modern Physics 4 Question 7

Modern Physics 4 Question 7

7. A particle $A$ of mass $m$ and initial velocity $v$ collides with a particle $B$ of mass $\frac{m}{2}$ which is at rest. The collision is held on, and elastic. The ratio of the de-Broglie wavelengths $λ_{A}$ to $λ_{B}$ after the collision is

(2017 Main)

(a) $\frac{λ_{A}}{λ_{B}} = 2$

(b) $\frac{λ_{A}}{λ_{B}} = \frac{2}{3}$

(d) $\frac{λ_{A}}{λ_{B}} = \frac{1}{3}$

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Solution:

For elastic collision,

$\begin{aligned} p_{before collision} & = p_{after collision} \\ m v & = m v_{A} + \frac{m}{2} v_{B} \\ 2 v & = 2 v_{A} + v_{B} \end{aligned}$

Now, coefficient of restitution,

$e = \frac{v_{B} - v_{A}}{u_{A} - v_{B}}$

Here, $u_{B} = 0$ (Particle at rest) and for elastic collisione $= 1$

$\begin{aligned} ∴ & 1 & = \frac{v_{B} - v_{A}}{v} \\ \Rightarrow & v & = v_{B} - v_{A} \end{aligned}$

From Eq. (i) and Eq. (ii)

$\begin{matrix} v_{A} = \frac{v}{3} and v_{B} = \frac{4 v}{3} \\ Hence, \frac{λ_{A}}{λ_{B}} = \frac{\frac{h}{m V_{A}}}{\frac{h}{\frac{m}{2} \cdot V_{B}}} = \frac{V_{B}}{2 V_{A}} = \frac{4 / 3}{2 / 3} = 2 \end{matrix}$

Modern Physics 4 Question 7

7. A particle $A$ of mass $m$ and initial velocity $v$ collides with a particle $B$ of mass $\frac{m}{2}$ which is at rest. The collision is held on, and elastic. The ratio of the de-Broglie wavelengths $λ_{A}$ to $λ_{B}$ after the collision is

Solution:

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Modern Physics 4 Question 7

7. A particle A of mass m and initial velocity v collides with a particle B of mass m2 which is at rest. The collision is held on, and elastic. The ratio of the de-Broglie wavelengths λA to λB after the collision is

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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7. A particle $A$ of mass $m$ and initial velocity $v$ collides with a particle $B$ of mass $\frac{m}{2}$ which is at rest. The collision is held on, and elastic. The ratio of the de-Broglie wavelengths $λ_{A}$ to $λ_{B}$ after the collision is