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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 - Physics

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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Solution 1

Let mm1, and m2 be the respective masses of the parent nucleus and the two daughter nuclei. The parent nucleus is at rest.

Initial momentum of the system (parent nucleus) = 0

Let v1 and v2 be the respective velocities of the daughter nuclei having masses m1and m2.

Total linear momentum of the system after disintegration = 'm_1v_1 + m_2v_2`

According to the law of conservation of momentum:

Total initial momentum = Total final momentum

`0 = m_1v_1 + m_2+v_2`

`v_1 =  (-m_2v_2)/m_1`

Here, the negative sign indicates that the fragments of the parent nucleus move in directions opposite to each other.

Solution 2

Let m1, m2 be the masses of products and v1,v2 be their respective velocities. Therefore, total linear momentum after disintegration = m1v1 +m2 v2. Before disintegration, the nucleus is at rest.

Therefore, its linear momentum before disintegration is zero.

According to the principle of conservation of linear momentum

`m_1vecv_1 + m_2vecv_2 = 0 or vecv_2 = - (m_1vecv_1)/m_2`

Negative sign shows that v1 and v2 are in opposite directions

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NCERT Class 11 Physics Textbook
Chapter 5 Laws of Motion
Q 17 | Page 111
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