SATHEE: Modern Physics 5 Question 10

Modern Physics 5 Question 10

10. A nucleus with mass number 220 initially at rest emits an $α$ -particle. If the $Q$ value of the reaction is $5.5 M e V$ , calculate the kinetic energy of the $α$ -particle

$(2003, 2 M)$

(a) $4.4 M e V$

(b) $5.4 M e V$

(d) $6.5 M e V$

Show Answer

Answer:

Correct Answer: 10. (b)

Solution:

Given that $K_{1} + K_{2} = 5.5 M e V$

From conservation of linear momentum,

$\begin{aligned} p_{1} = p_{2} \\ or & \sqrt{2 K_{1} (216 m)} & = \sqrt{2 K_{2} (4 m)} & as p = \sqrt{2 K m} \\ ∴ & K_{2} & = 54 K_{1} \end{aligned}$

Solving Eqs. (i) and (ii), we get

$K_{2} = K E$ of $α$ -particle $= 5.4 M e V$ .

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Modern Physics 5 Question 10

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

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10. A nucleus with mass number 220 initially at rest emits an $α$ -particle. If the $Q$ value of the reaction is $5.5 M e V$ , calculate the kinetic energy of the $α$ -particle