A nucleus with mass number 184 initially at rest emits an -particle. If the Q value of the reaction is 5.5 MeV, calculate the kinetic energy of the -particle

Question

A nucleus with mass number 184 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

Smart Achievers · Accepted Answer

(4)

$\frac{1}{2} (4 m) v^{2} + \frac{1}{2} (180 m) {(\frac{4 v}{180})}^{2} = 5.5 M e V$

$\frac{1}{2} (4 m v^{2}) [1 + 45 {(\frac{4}{180})}^{2}] = 5.5 M e V$

$\Rightarrow K . E ._{α} = \frac{5.5}{1 + 45 {(\frac{4}{180})}^{2}} M e V$

$K . E ._{α} = 5.38 M e V$

Solution

Q.
A nucleus with mass number 184 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

1 5 MeV

2 5.5 MeV

3 0.12 MeV

4 5.38 MeV

Ans.
(4)

$\frac{1}{2} (4 m) v^{2} + \frac{1}{2} (180 m) {(\frac{4 v}{180})}^{2} = 5.5 M e V$

$\frac{1}{2} (4 m v^{2}) [1 + 45 {(\frac{4}{180})}^{2}] = 5.5 M e V$

$\Rightarrow K . E ._{α} = \frac{5.5}{1 + 45 {(\frac{4}{180})}^{2}} M e V$

$K . E ._{α} = 5.38 M e V$

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