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NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Physics
Chapter: Atomic Physics

NTA Abhyas 2020 · Physics · Atomic Physics

A travelling nucleus A having a de-Broglie wavelength λ _ A...

A travelling nucleus

A

having a de-Broglie wavelength

{λ}_{A}

spontaneously splits into two nuclei

B

and

C

of equal masses. After the split,

B

travels in the same direction while

C

travels in the opposite direction with a speed equal to half of

B

. The values of the de-Broglie wavelengths

{λ}_{B}

and

{λ}_{C}

& will be

Options

A ${λ}_{A}, 2{λ}_{A}$
B $\dfrac{\lambdaA}{2}, {λ}_{A}$
C ${λ}_{A}, \dfrac{\lambdaA}{2}$
D $2{λ}_{A}, {λ}_{A}$

Correct answer

B. $\dfrac{\lambdaA}{2}, {λ}_{A}$

Step-by-step solution

$\begin{cases}A \to u & {←}^{v / 2}C & B \to v \\ 2m & m & m\end{cases}$

Applying conservation of linear momentum

$2mu = mv - \dfrac{mv}{2}$

So,

${λ}_{A} = \dfrac{h}{2mu}{λ}_{B} = \dfrac{h}{mv} = \dfrac{\lambdaA}{2}{λ}_{C} = \dfrac{h}{m\dfrac{v}{2}} = {λ}_{A}$

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