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Question: Answered & Verified by Expert
An alpha particle $\left({ }^{4} \mathrm{He}\right)$ has a mass of 4.00300 amu. A proton has a mass of 1.00783 amu and a neutron has a mass of 1.00867 amu respectively. The binding energy of alpha estimated from these data is the closest to
PhysicsNuclear PhysicsWBJEEWBJEE 2013
Options:
  • A $27.9 \mathrm{MeV}$
  • B $22.3 \mathrm{MeV}$
  • C $35.0 \mathrm{MeV}$
  • D $20.4 \mathrm{MeV}$
Solution:
2595 Upvotes Verified Answer
The correct answer is: $27.9 \mathrm{MeV}$
The mass defect, $\Delta m=2\left(m_{p}+m_{n}\right)-m_{\text {He }}$
$=2(1.00783+1.00867)-4.00300$
$=0.0300$ amu
So, the binding energy, $E=\Delta m c^{2}$
$=0.03 \times 931 \mathrm{MeV}=27.9 \mathrm{MeV}$

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