A nucleus with mass number 220, initially at rest, emits an -particle. If the Q-value of the reaction is 5.5 MeV, calculate the kinetic energy of the -particle. [2003]

Question

A nucleus with mass number 220, initially at rest, emits an $α$ -particle. If the Q-value of the reaction is 5.5 MeV, calculate the kinetic energy of the $α$ -particle. [2003]

Smart Achievers · Accepted Answer

(2)

By conservation of momentum, $α$

$\sqrt{2 K_{1} m_{1}} = \sqrt{2 K_{2} m_{2}}$ $[∵ P = \sqrt{2 K m}]$

$\Rightarrow \sqrt{2 K_{1} (216)} = \sqrt{2 K_{2} (4)}$

$∴$ $K_{2} = 54 K_{1}$ $\dots (i)$

And given, $K_{1} + K_{2} = 5.5 MeV$ $\dots (i i)$

Solving equations (i) and (ii), we get $K_{α} = K_{2} = 5.4 MeV$

Solution

Q.
A nucleus with mass number 220, initially at rest, emits an $α$ -particle. If the Q-value of the reaction is 5.5 MeV, calculate the kinetic energy of the $α$ -particle. [2003]

1 4.4 MeV

2 5.4 MeV

3 5.6 MeV

4 6.5 MeV

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