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Concepts Of Physics MCQ Edition [Volume 2]
Exam
Concepts Of Physics MCQ Edition [Volume 2]
Subject
Physics
Chapter
The Nucleus

Concepts Of Physics MCQ Edition [Volume 2] · Physics · The Nucleus

A free neutron undergoes beta-decay to a proton, having a half-life...

A free neutron undergoes beta-decay to a proton, having a half-life of 14 minutes14 \text{ minutes}. Calculate the energy liberated during this process.

Options

  1. A279 keV279 \text{ keV}
  2. B782 keV782 \text{ keV}
  3. C931 keV931 \text{ keV}
  4. D511 keV511 \text{ keV}

Correct answer

B. 782 keV782 \text{ keV}

Step-by-step solution

The beta-decay of a free neutron is represented by the equation:

n→p+e−+νˉen \rightarrow p + e^{-} + \bar{\nu}_{e}

The energy liberated (QQ-value) during this process is given by the mass defect:

Q=(mn−mp−me)c2Q = (m_{n} - m_{p} - m_{e})c^{2}

Using the standard rest mass energies:
Rest mass energy of neutron, mnc2=939.565 MeVm_{n}c^{2} = 939.565 \text{ MeV}
Rest mass energy of proton, mpc2=938.272 MeVm_{p}c^{2} = 938.272 \text{ MeV}
Rest mass energy of electron, mec2=0.511 MeVm_{e}c^{2} = 0.511 \text{ MeV}

Substituting these values:

Q=939.565−938.272−0.511Q = 939.565 - 938.272 - 0.511

Q=0.782 MeVQ = 0.782 \text{ MeV}

Q=782 keVQ = 782 \text{ keV}

The half-life of 14 minutes14 \text{ minutes} is extra information not required for this calculation.
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