Question

A radioactive nucleus of mass number A, initially
at rest, emits an a-particle with a speed v. The
recoil speed of daughter nucleus is
(a) 2 ???? (b) 2 ????
A - 4 A + 4
(c) 4 ???? (d) 4 ????
A - 4 A + 4

Answer 1

Answer:

PHYSICS

A radioactive nucleus of mass number A, initially at rest, emits an α-particle with a speed v. The recoil speed of the daughter

Explanation:

ANSWER

Mass of radioactive nucleus, $$M = mA$$ where, m is the mass of one proton

Mass number of the α (He) particle is 4 and that of daughter nucleus is A−4

∴ Mass of daughter nucleus, M

′

=(A−4)m

Mass of α particle, $$M_{\alpha} =4m$$

Let the recoil speed of daughter nucleus be, v

R

Applying conservation of momentum :

$$\Rightarrow 0 = M_{\alpha} (v) - M' (v_R)$$

$$\Rightarrow 0 = 4m v - (A-4) mv_R$$

$$\Rightarrow v_R = \dfrac{4v}{A-4}$$

solution