Question 7 of 13intermediate🔧 ApplyNumerical3 marks

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 2963Cu^{63}_{29}\text{Cu} atoms (of mass 62.92960 u).

Correct Answer

The nuclear energy required to separate all neutrons and protons is approximately 2.5×102.5 \times 10¹² J.

Exercise: EXERCISES | Q: 13.3 | (Page 16)
For More Understanding

Explanation

This question requires calculating the total binding energy of all copper nuclei in the coin. The binding energy per nucleus is found using the mass defect method, then multiplied by the total number of atoms in the coin.

Solution Steps

  1. Step 1: Find the number of Cu atoms in the coin Number of atoms = (Mass of coin / Molar mass) × Avogadro's number = (3.0 g / 63 g/mol) × 6.023×106.023 \times 10²³ = 2.87×102.87 \times 10²² atoms

  2. Step 2: Calculate mass defect for one Cu nucleus For ²⁹³Cu: Z = 29 protons, N = 63 - 29 = 34 neutrons Mass of constituents = 29 × m_H + 34 × m_n = 29×1.00782529 \times 1.007825 + 34×1.00866534 \times 1.008665 = 29.226925 + 34.29461 = 63.521535 u Mass defect Δm = 63.521535 - 62.92960 = 0.591935 u

  3. Step 3: Calculate binding energy per nucleus Binding energy = Δm × 931.5 MeV/u = 0.591935×931.50.591935 \times 931.5 = 551.4 MeV

  4. Step 4: Calculate total binding energy Total energy = Number of atoms × Binding energy per nucleus = 2.87×102.87 \times 10²² × 551.4 MeV = 1.58×101.58 \times 10²⁵ MeV

  5. Step 5: Convert to Joules Total energy = 1.58×101.58 \times 10²⁵ × 1.6×101.6 \times 10⁻¹³ J = 2.53×102.53 \times 10¹² J

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