# A nucleus with mass number 220 initially at rest, emits an alpha particle. If the Q value of the reaction…

Q: 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 K.E. of the alpha particles.

(a) 4.4 MeV

(b) 5.4 MeV

(c) 5·6 MeV

(d) 6·5 MeV

Ans:(b)

Sol: From conservation of linear momentum,

pi = pf

As Linear Momentum $\displaystyle p = \sqrt{2 m E}$

$\displaystyle 0 = \sqrt{2 (216 m) E_1} - \sqrt{2 (4 m) E_2}$ (since , moves in opposite direction )

$\displaystyle \sqrt{2 (216 m) E_1} = \sqrt{2 (4 m) E_2}$

E2 = 54 E1

As, E1 + E2 = 5.5 MeV

E1 + 54 E1 = 5.5 MeV

55 E1 = 5.5 MeV

E1 = 0.1 MeV

Hence , E2 = 5.4 MeV

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