A radioactive nucleus of mass number A , initially at rest, emits on α -particle with a speed v . What will be the recoil speed of the daughter nucleus?

Question

A radioactive nucleus of mass number A , initially at rest, emits on α -particle with a speed v . What will be the recoil speed of the daughter nucleus? (A) (2 v/(. A - 4 .)) (B) (2 v/(. A + 4 .)) (C) (4 v/(. A - 4 .)) (D) (4 v/(. A + 4 .))

Tardigrade Admin · Accepted Answer

Given that, the radioactive nucleus of mass number

A

, initially at rest, emits an

α

- particle with a speed

v

.
From conservation of linear momentum,
Initial moment before reaction

=

final momentum after reaction

0 = 4 v - (A - 4) v_{1}

\Rightarrow v_{1} = (\frac{4 v}{A - 4})

The recoil speed of the daughter nucleus will be

= (\frac{4 v}{A - 4})

Q. A radioactive nucleus of mass number $A$ , initially at rest, emits on $α$ -particle with a speed $v$ . What will be the recoil speed of the daughter nucleus?

$\frac{2 v}{( A - 4 )}$

$\frac{2 v}{( A + 4 )}$

$\frac{4 v}{( A - 4 )}$

$\frac{4 v}{( A + 4 )}$

Q. A radioactive nucleus of mass number A , initially at rest, emits on α -particle with a speed v . What will be the recoil speed of the daughter nucleus?

(A−4)2v​

(A+4)2v​

(A−4)4v​

(A+4)4v​

Q. A radioactive nucleus of mass number $A$ , initially at rest, emits on $α$ -particle with a speed $v$ . What will be the recoil speed of the daughter nucleus?

$\frac{2 v}{( A - 4 )}$

$\frac{2 v}{( A + 4 )}$

$\frac{4 v}{( A - 4 )}$

$\frac{4 v}{( A + 4 )}$