A nucleus with mass number 184 initially at rest emits an α -...

A nucleus with mass number

184

initially at rest emits an

\alpha -

particle. If the

Q

value of the reaction is

5 . 5MeV,

calculate the kinetic energy of the

\alpha -

particle.

Options

A $5 . 0MeV$
B $5 . 5MeV$
C $0 . 12MeV$
D $5 . 38MeV$

Correct answer

D. $5 . 38MeV$

Step-by-step solution

A nucleus with mass number 184 initially at rest emits an α - particle. If the Q value of the reaction is 5 . 5MeV,

$\dfrac{1}{2}\left(4m\right){v}^{2} + \dfrac{1}{2}\left(180m\right){\left(\dfrac{4v}{180}\right)}^{2} = 5 . 5MeV$

$⇒ \dfrac{1}{2}4{mv}^{2}\left[1 + 45{\left(\dfrac{4}{180}\right)}^{2}\right] = 5 . 5MeV$
$⇒ K . E{.}_{\alpha} = \dfrac{5 . 5}{1 + 45 \cdot {\left(\dfrac{4}{180}\right)}^{2}}MeV = 5 . 38MeV$

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