A nucleus with mass number `220` initially at rest emits an `alpha`-particle. If the Q-value of the reaction is `5.5 MeV`, calculate the kinetic energy of the `alpha`-particle.
(a) 4.4 MeV (b) 5.4 MeV (c) 5.6 MeV (d) 6.5 MeV

Options

A. `4.4 MeV`
B. `5.4 MeV`
C. `5.6 MeV`
D. `6.5 MeV`

Answer

B

Explanation

`K_(1)+K_(2)=5.5 MeV`
From conservation of linear momentum
`[2K_(1),(216m)]^(1//2)[2K_(2)(4m)]^(1//2) , K_(2)=54K_(1)`
From the above `K_(2)=5.4 MeV`