Question:

When $U^{238}$ nucleus originally at rest, decays by emitting an alpha particle having a speed u, the recoil speed of the residual nucleus is

Updated On: Jul 2, 2022
  • $\frac{4u}{238}$
  • $-\frac{4u}{234}$
  • $\frac{4u}{234}$
  • $-\frac{4u}{238}$
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The Correct Option is D

Solution and Explanation

According to principle of conservation of linear momentum the momentum of the system remains the same before and after the decay. Atomic mass of uranium = 238 and after emitting an alpha particle $= 238 - 4 = 234$ $? 238 ? 0 = 4u + 234 v$ $\therefore v=-\frac{4u}{234}$
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Concepts Used:

Nuclei

In the year 1911, Rutherford discovered the atomic nucleus along with his associates. It is already known that every atom is manufactured of positive charge and mass in the form of a nucleus that is concentrated at the center of the atom. More than 99.9% of the mass of an atom is located in the nucleus. Additionally, the size of the atom is of the order of 10-10 m and that of the nucleus is of the order of 10-15 m.

Read More: Nuclei

Following are the terms related to nucleus:

  1. Atomic Number
  2. Mass Number
  3. Nuclear Size
  4. Nuclear Density
  5. Atomic Mass Unit