5.17 A nucleus is at rest in the laboratory frame of reference. Show that if it disintegrates into two smaller nuclei the products must move in opposite directions.

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Vishal Baghel | Contributor-Level 10

4 months ago

Let m₁ & m₂ be the masses of two nuclei and m be the mass of the main nuclei.

m = m₁ + m₂

If $v_{1}$ and $v_{2}$ be the corresponding velocities of two nuclei then total linear momentum after disintegration = m₁ $v_{1}$ + m₂ $v_{2}$

Since at the initial stage, mass nuclei was at rest, so the initial linear momentum = 0

From the law of conservation we know

Total linear momentum before disintegration = total momentum after disintegration

0 = m₁ $v_{1}$ + m₂ $v_{2}$

$v_{1}$ = - m₂ $v_{2}$ / m₁

-ve sign indicates that the two velocities $v_{1}$ and $v_{2}$ are in opposite direction

<div><div>Let m1 & m2 be the masses of two nuclei and m be the mass of the main nuclei.</div></div>m = m1 + m2If <math><msub><mrow><mrow><mi>v</mi></mrow></mrow><mrow><mrow><mn>1</mn></mrow></mrow></msub></math> and <math><msub><mrow><mrow><mi>v</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msub></math> be the corresponding velocities of two nuclei then total linear momentum after disintegration = m1 <math><msub><mrow><mrow><mi>v</mi></mrow></mrow><mrow><mrow><mn>1</mn></mrow></mrow></msub></math> + m2 <math><msub><mrow><mrow><mi>v</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msub></math>Since at the initial stage, mass nuclei was at rest, so the initial linear momentum = 0From the law of conservation we knowTotal linear momentum before disintegration = total momentum after disintegration0 = m1<math><msub><mrow><mrow><mi>v</mi></mrow></mrow><mrow><mrow><mn>1</mn></mrow></mrow></msub></math> + m2<math><msub><mrow><mrow><mi>v</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msub></math><math><msub><mrow><mrow><mi>v</mi></mrow></mrow><mrow><mrow><mn>1</mn></mrow></mrow></msub></math> = - m2<math><msub><mrow><mrow><mi>v</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msub></math> / m1-ve sign indicates that the two velocities <math><msub><mrow><mrow><mi>v</mi></mrow></mrow><mrow><mrow><mn>1</mn></mrow></mrow></msub></math> and <math><msub><mrow><mrow><mi>v</mi></mrow></mrow><mrow><mrow><mn>2</mn></mrow></mrow></msub></math> are in opposite direction

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5.17 A nucleus is at rest in the laboratory frame of reference. Show that if it disintegrates into two smaller nuclei the products must move in opposite directions.

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