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 <math><mmultiscripts><mrow><mrow><mi mathvariant="bold-italic">C</mi><mi mathvariant="bold-italic">u</mi></mrow></mrow><mprescripts></mprescripts><mrow><mrow><mn>29</mn></mrow></mrow><mrow><mrow><mn>63</mn></mrow></mrow></mmultiscripts></math> atoms (of mass 62.92960 u).

13.5 Mass of the copper coin, m’ = 3.0 gAtomic mass of Cu2963 , m = 62.92960 uThe total number of Cu2963 atoms in the coin, N = NA×m'Massnumber , whereNA = Avogadro’s number = 6.023 ×1023 atoms / gMass number = 63 gTherefore, N = 6.023×1023×363 = 2.868 ×1022 atomsCu2963 has 29 protons and (63 – 29) 34 neutronsHence the mass defect of the nucleus Δm = 29 ×mp + 34 ×mn - mMass of a proton, mp = 1.007825 uMass of a neutron, mn = 1.008665 uΔm = 29 ×1.007825 + 34 ×1.008665 - 62.92960Δm = 0.591935 uMass defect of all the atoms present in the coin, Δm = 0.591935 ×N= 0.591935 × 2.868 ×1022 = 1.69766958 ×1022 uBut 1 u = 931.5 MeV/ c2Δm = 1.581 ×1025 MeV/ c2The binding energy of the nucleus, Eb = Δm c2 , where c = speed of lightEb= (1.581 ×1025 / c2 ) × c2 = 1.581 ×1025 MeV1 MeV = 1.6 ×10-13 JHence, Eb= 2.530 ×1012 JThis much of energy required to separate all the neutrons and protons from the given coin.

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Physics Ncert Solutions Class 12th Physics Class 12th Nuclei

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 ${}_{29}^{63}{C u}$ atoms (of mass 62.92960 u).

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Payal Gupta | Contributor-Level 10

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13.5 Mass of the copper coin, m’ = 3.0 g

Atomic mass of ${}_{29}^{63}{C u}$ , m = 62.92960 u

The total number of ${}_{29}^{63}{C u}$ atoms in the coin, N = $\frac{N_{A} \times m'}{M a s s n u m b e r}$ , where

$N_{A}$ = Avogadro’s number = 6.023 $\times 10^{23}$ atoms / g

Mass number = 63 g

Therefore, N = $\frac{6.023 \times 10^{23} \times 3}{63}$ = 2.868 $\times 10^{22}$ atoms

${}_{29}^{63}{C u}$ has 29 protons and (63 – 29) 34 neutrons

Hence the mass defect of the nucleus Δm = 29 $\times m_{p}$ + 34 $\times m_{n}$ - $m$

Mass of a proton, $m_{p}$ = 1.007825 u

Mass of a neutron, $m_{n}$ = 1.008665 u

Δm = 29 $\times 1.007825$ + 34 $\times 1.008665$ - 62.92960

Δm = 0.591935 u

Mass defect of all the atoms present in the coin, Δm = 0.

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13.5 Mass of the copper coin, m’ = 3.0 g

Atomic mass of ${}_{29}^{63}{C u}$ , m = 62.92960 u

The total number of ${}_{29}^{63}{C u}$ atoms in the coin, N = $\frac{N_{A} \times m'}{M a s s n u m b e r}$ , where

$N_{A}$ = Avogadro’s number = 6.023 $\times 10^{23}$ atoms / g

Mass number = 63 g

Therefore, N = $\frac{6.023 \times 10^{23} \times 3}{63}$ = 2.868 $\times 10^{22}$ atoms

${}_{29}^{63}{C u}$ has 29 protons and (63 – 29) 34 neutrons

Hence the mass defect of the nucleus Δm = 29 $\times m_{p}$ + 34 $\times m_{n}$ - $m$

Mass of a proton, $m_{p}$ = 1.007825 u

Mass of a neutron, $m_{n}$ = 1.008665 u

Δm = 29 $\times 1.007825$ + 34 $\times 1.008665$ - 62.92960

Δm = 0.591935 u

Mass defect of all the atoms present in the coin, Δm = 0.591935 $\times N$

= 0.591935 $\times$ 2.868 $\times 10^{22}$ = 1.69766958 $\times 10^{22}$ u

But 1 u = 931.5 MeV/ $c^{2}$

Δm = 1.581 $\times 10^{25}$ MeV/ $c^{2}$

The binding energy of the nucleus, $E_{b}$ = Δm $c^{2}$ , where c = speed of light

$E_{b} =$ (1.581 $\times 10^{25}$ / $c^{2}$ ) $\times$ $c^{2}$ = 1.581 $\times 10^{25}$ MeV

1 MeV = 1.6 $\times 10^{- 13}$ J

Hence, $E_{b} =$ 2.530 $\times 10^{12}$ J

This much of energy required to separate all the neutrons and protons from the given coin.

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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 ${}_{29}^{63}{C u}$ atoms (of mass 62.92960 u).

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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 Cu2963 atoms (of mass 62.92960 u).

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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 ${}_{29}^{63}{C u}$ atoms (of mass 62.92960 u).