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>>Nuclei
>>Alpha Beta and Gamma Decay
>> $A stationary thorium nucleus (A = 220, Z$

Question

A stationary thorium nucleus $(A = 220, Z = 90)$ emits an alpha particle with kinetic energy $E_{α}$ . What is the kinetic energy of the recoiling nucleus?

A

$\frac{E _{α}}{1 0 8}$

B

$\frac{E _{α}}{1 1 0}$

C

$\frac{E _{α}}{5 5}$

D

$\frac{E _{α}}{5 4}$

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Updated on : 2022-09-05

Solution

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Correct option is D)

$^{220} Z_{90} \to α + X$
$m_{X} = 220 - m_{α} = 216$

$E = \frac{p ^{2}}{2 m}$
$p = 2 m E$

Momentum Conservation:
$2 m_{α} E_{α} = 2 m_{X} E_{X}$
$m_{α} E_{α} = m_{X} E_{X}$
$4 E_{α} = 216 E_{X}$
$E (X) = \frac{E _{α}}{5 4}$

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