Question

What will be the speed of this recoiling nucleus if the speed of the alpha particle is 3.4×105 m/s ? assume the recoiling nucleus has a mass 57 times greater than that of the alpha particle?

Answer 1

here initially before the recoil of nucleus the system is considered to be at rest

now by the conservation of momentum we can say

$P_f = P_i$

$m_1v_1 + m_2v_2 = 0$

now we know that

$m_1 = 57 m_2$

also it is given that

speed of alpha nucleus is 3.4 * 10^5 m/s

$v_2 = 3.4 * 10^5 m/s$

now by the momentum conservation equation we will have

$57m_2* v_2 = -m_2*3.4*10^5$

$v_2 = -\frac{3.4 * 10^5}{57} = -5.9 * 10^3 m/s$

so the recoil speed will be given as 5.9 * 10^3 m/s