A nucleus splits into two nuclear fragments. | vedclass

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Question

(D) According to the law of conservation of linear momentum,for a nucleus initially at rest,the magnitudes of momenta of the two fragments must be equ

Vedclass · Accepted Answer

$1:2^{1/3}$

Vedclass · Answer

(D) According to the law of conservation of linear momentum,for a nucleus initially at rest,the magnitudes of momenta of the two fragments must be equal: $m_1 v_1 = m_2 v_2$.Therefore,the ratio of masses is inversely proportional to the ratio of velocities: $\frac{m_1}{m_2} = \frac{v_2}{v_1}$.Given $\frac{v_1}{v_2} = \frac{2}{1}$,we have $\frac{m_1}{m_2} = \frac{1}{2}$.The nuclear radius $R$ is related to the mass number $A$ (which is proportional to mass $m$) by the formula $R = R_0 A^{1/3}$.Thus,the ratio of radii is $\frac{R_1}{R_2} = \left(\frac{A_1}{A_2}\right)^{1/3} = \left(\frac{m_1}{m_2}\right)^{1/3}$.Substituting the mass ratio: $\frac{R_1}{R_2} = \left(\frac{1}{2}\right)^{1/3} = \frac{1}{2^{1/3}}$.Hence,the ratio is $1:2^{1/3}$.

$A$ nucleus splits into two nuclear fragments. If the ratio of their velocities is $2:1$,then the ratio of their nuclear radii is:

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