Question

An $\alpha$ particle is emitted from a stationary ${}_{92}{U}^{238}$ nucleus with a velocity of $2.34\times {10}^{4}m{S}^{-1}$. Find the recoil velocity of the daughter nucleus.

• A. $-300m{s}^{-1}$
• B. $-200m{S}^{-1}$
• C. $-100m{s}^{-1}$
• D. $-400m{s}^{-1}$

Answer 1

The correct option is D $-400m{s}^{-1}$

Using conservation of linear momentum

$M_1{V}_1=M_2{V}_2$

$M_1\to$ Mass of $\alpha$ particles, $V_1\to$ Velocity of $\alpha$ particle, $M_2\to$ Mass of Uranium, $V_2\to$ Velocity of Uranium

$4\times 2.34\times {10}^4=238\times V_2{V}_2=\frac{4\times 2.34\times {10}^4}{238}\approx 400m/s$
There will be negative sign since recoil velocity will be in opposite direction.

So, $V_2=-400m/s$