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.

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. (A) 5.0 MeV (B) 5.5 MeV (C) 0.12 MeV (D) 5.38 MeV

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/32521138cc983a775ae771897263f829-.png" /> (1/2)(4 m) v2+(1/2)(180 m)((4 v/180))2=5.5 MeV ⇒ (1/2) 4 m v2[1+45((4/180))2]=5.5 MeV ⇒ K . Ea=(5.5/1+45 ⋅((4)180)2) MeV K ⋅ Eα=5.38 MeV

Q. A nucleus with mass number $184$ 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.

5.0 MeV

5.5 MeV

0.12 MeV

5.38 MeV

$\frac{1}{2} (4 m) v^{2} + \frac{1}{2} (180 m) (\frac{4 v}{180})^{2} = 5.5 M e V$
$\Rightarrow \frac{1}{2} 4 m v^{2} [1 + 45 (\frac{4}{180})^{2}] = 5.5 M e V$
$\Rightarrow K . E_{a} = \frac{5.5}{1 + 45 \cdot ( \frac{4}{180} ) ^{2}} M e V$
$K \cdot E_{α} = 5.38 M e V$

Q. A nucleus with mass number 184 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.