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A nucleus X initially at rest, undergoes...

A nucleus X initially at rest, undergoes alpha decay according to the equation
`_Z^232Xrarr_90^AY+alpha`
What fraction of the total energy released in the decay will be the kinetic energy of the alpha particle?

A

(a) `90/92`

B

(b) `228/232`

C

(c) `sqrt(228/232)`

D

(d) `1/2`

Text Solution

Verified by Experts

The correct Answer is:
B
`A=232-4=228`
From conservation of momentum,
`p_alpha=p_gamma=sqrt(2K_alpham_alpha)=sqrt(2K_gammam_gamma)`
or `(K_alpha)/(K_gamma)=(m_gamma)/(m_alpha)=228/4`
`:.` `K_alpha=((228)/(228+4))K_(t otal)`
`=(228/232)K_(T otal)`
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