Answer to Question #290001 in Atomic and Nuclear Physics for Sally

Question

In a radioactive decay, a nucleus of mass 4.0 × 10-25kg initially at rest emitted an a-particle of mass 6.7 x 10-27kg with a velocity of 1.5 x 107 ms-¹.

a Calculate the velocity of recoil of the nucleus.

b Calculate the kinetic energy of:

1 the recoil nucleus,

ii the o-particle.

Answer 1

a. By conservation of momentum:

$$0=m_nv+m_pu→v=u\dfrac{m_p}{m_n}=251250\text{ m/s}.$$

b i. The kinetic energy of the recoil nucleus:

$$KE_n=\dfrac12m_nv^2=1.26·10^{-14}\text{ J}.$$

b i. The kinetic energy of the particle:

$$KE_p=\dfrac12m_pv^2=7.54·10^{-13}\text{ J}.$$