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  • A given coin has a mass of 3.0 g. Calculate the nuclear energy that would be required to separate all the neutrons and protons from each other For simplicity assume that the coin is entirely made of 63 29 Cu atoms (of mass 62.92960 u).

Q.13.5 A given coin has a mass of 3.0\; g. Calculate the nuclear energy that would be required to separate all the neutrons and protons from each other. For simplicity assume that the coin is entirely made of _{29}^{63}\textrm{Cu}  atoms (of mass 62.92960\; \; u).

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Mass of the coin is w = 3g

Total number of Cu atoms in the coin is n

 \\n=\frac{w\times N_{A}}{Atomic\ Mass}\\ n=\frac{3\times 6.023\times 10^{23}}{62.92960}

n=2.871\times1022

mH = 1.007825 u

mn = 1.008665 u

Atomic mass of _{29}^{63}\textrm{Cu} is m=62.92960 u

Mass defect \Deltam=(63-29)\timesmn+29\timesmH - m

\Deltam=34\times1.008665+29\times1.007825 - 62.92960

\Deltam=0.591935 u

Now 1u is equivalent to 931.5 MeV

Eb=0.591935\times931.5

Eb=551.38745 MeV

Therefore binding energy of a _{29}^{63}\textrm{Cu} nucleus is 551.38745 MeV.

The nuclear energy that would be required to separate all the neutrons and protons from each other is

n\timesEb=2.871\times1022\times551.38745

=1.5832\times1025 MeV

=1.5832\times1025\times1.6\times10-19\times106J

=2.5331\times109 kJ

 

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Sayak

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