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Physics - Modern Physics Question with Solution | TestHub

PhysicsModern PhysicsAtomic structureEasy2 minPYQ_2020

PhysicsEasysingle choice

The distance of closest approach of an $α$ particle fired towards a nucleus with momentum $p$ is $r$ . If the momentum of the $α$ particle is $2 p$ , the corresponding distance of closest approach is

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Answer:

Solution:

At the distance of closest approach, r

$K = \frac{1}{4 π ε_{0}} . \frac{2 e Z e}{r}$

$r = \frac{1}{4 π ε_{0}} . \frac{2 Z e^{2}}{K}$

$∵ K = \frac{P^{2}}{2 m}$

$∴ r = \frac{4}{4 π ε_{0}} . \frac{2 Z e^{2}}{\frac{p^{2}}{2 m}}$

$= \frac{1}{4 π ε_{0}} . \frac{4 m Z e^{2}}{p^{2}}$

Thus, $r \propto \frac{1}{p^{2}}$

$∴ \frac{r_{1}}{r_{2}} = \frac{p_{2}^{2}}{p_{1}^{2}} = \frac{{(2 p)}^{2}}{p^{2}}$

$\frac{r_{1}}{r_{2}} = \frac{4}{1} \Rightarrow ∴ r_{2} = \frac{r_{1}}{4} = \frac{r}{4}$

Stream:NTA_ABHYAS_NEETSubject:PhysicsTopic:Modern PhysicsSubtopic:Atomic structure

⏱ 2mℹ️ Source: PYQ_2020

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