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

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 , then calculate the kinetic energy of the α -particle. (A) 4.4 MeV (B) 5.4 MeV (C) 5.6MeV (D) 6.5MeV

Tardigrade Admin · Accepted Answer

Given that K1+K2= text5.5 MeV ... (i) From conservation of linear momentum, p1=p2 √2 K1 (. 216 m .) = √2 K2 (. 4 m .) (As p = √2 K m ) K2=54K1 ... (ii) Solving Eqs. (i) and (ii), we get K2= K.E. of α -particle text5.4 MeV .

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

$4.4 M e V$

$5.4 M e V$

$5.6 M e V$

$6.5 M e V$

Given that $K_{1} + K_{2} = 5.5 M e V$ ... (i)
From conservation of linear momentum,
$p_{1} = p_{2}$
$2 K_{1} (216 m) = 2 K_{2} (4 m)$ (As $p = 2 K m$ )
$K_{2} = 54 K_{1}$ ... (ii)
Solving Eqs. (i) and (ii), we get
$K_{2} =$ K.E. of $α$ -particle $5.4 M e V$ .

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

4.4MeV

5.4MeV

5.6MeV

6.5MeV