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# A Uranium-238 Nucleus, Initially at Rest, Emits an Alpha Particle with a Speed of 1.4 × 107m/S. Calculate the Recoil Speed of the Residual - Physics

Sum

A uranium-238 nucleus, initially at rest, emits an alpha particle with a speed of 1.4 × 107m/s. Calculate the recoil speed of the residual nucleus thorium-234. Assume that the mass of a nucleus is proportional to the mass number.

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#### Solution

According to the question, uranium 238 nucleus emits an alpha-particle with a speed of 1.4 × 107 m/s.
Let the speed of the residual nucleus thorium 234 be v2.

By the law of conservation of linear momentum, we have:
$m_1 v_1 = m_2 v_2$
Here, m1 and v1 are the mass and velocity of the alpha-particle repectively, and m2 is the mass of the residual nucleus.

$\Rightarrow 4 \times 1 . 4 \times {10}^7 = 234 \times v_2$

$v_2 = \frac{4 \times 1 . 4 \times {10}^7}{234} = 2 . 4 \times {10}^5 \text{ m/s }$
Therefore, the speed of the residual nucleus is
$2 . 4 \times {10}^5 \text{ m/s}$

Concept: Momentum Conservation and Centre of Mass Motion
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#### APPEARS IN

HC Verma Class 11, 12 Concepts of Physics 1
Chapter 9 Centre of Mass, Linear Momentum, Collision
Q 16 | Page 160
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