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

Question #290001

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.

1
Expert's answer
2022-01-23T16:13:30-0500

a. By conservation of momentum:


0=mnv+mpuv=umpmn=251250 m/s.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:


KEn=12mnv2=1.261014 J.KE_n=\dfrac12m_nv^2=1.26·10^{-14}\text{ J}.


b i. The kinetic energy of the particle:


KEp=12mpv2=7.541013 J.KE_p=\dfrac12m_pv^2=7.54·10^{-13}\text{ J}.


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