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Binding Energy

Calculate the...

Question

Calculate the binding energy per nucleon for Beryllium $_{4} {B e}^{9}$ , its mass being $9.012 u$ . The masses of proton and neutron are $1.008 u$ and $1.009 u$ . (Take $1 u = 931.5 M e V$ )

8.3636 MeV

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7.2828 MeV

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9.4444 MeV

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6.7275 MeV

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Solution

The correct option is D 6.7275 MeV
First, let us find the mass defect. The Beryllium nucleus contains 4 protons and 5 neutrons.
Mass of 4 protons $= 4 \times 1.008 = 4.032 u$ ; Mass of 5 neutrons $= 5 \times 1.009 u = 5.045 u$
Total mass of protons (4) and neutrons (5) $= 4.032 + 5.045 = 9.077 u$
Mass defect $= 9.077 - 9.012 = 0.065 u$
The mass defect converted into equivalent energy gives binding energy.
$1 u = 931.5 M e V$
$∴ 0.065 u = 0.065 \times 931.5 M e V = 60.5475 M e V$
Binding energy per nucleon $= \frac{B i n d i n g e n e r g y}{N u m b e r o f n u c l e o n s} = \frac{60.5475}{9} = 6.7275 M e V$

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