Question 3 of 13intermediate🔧 ApplyNumerical3 marks

Find the energy equivalent of one atomic mass unit, first in Joules and then in MeV. Using this, express the mass defect of 816O^{16}_{8}\text{O} in MeV/c2c^2.

Correct Answer

Step 1: Energy equivalent of 1 u in Joules

Given: 1 u = 1.6605×101.6605 \times 10⁻²⁷ kg

Energy equivalent = mass × c² = 1.6605×101.6605 \times 10⁻²⁷ × (2.9979×102.9979 \times 10⁸)² = 1.6605×101.6605 \times 10⁻²⁷ × 8.9874×108.9874 \times 10¹⁶ = 1.4924×101.4924 \times 10⁻¹⁰ J

Step 2: Energy equivalent of 1 u in MeV

Energy in eV = Energy in Joules / charge of electron = (1.4924×101.4924 \times 10⁻¹⁰) / (1.602×101.602 \times 10⁻¹⁹) = 0.9315×100.9315 \times 10⁹ eV = 931.5 MeV

Thus, 1 u = 931.5 MeV/c²

Step 3: Mass defect of ¹⁶₈O in MeV/c²

Given: Mass defect (ΔM) = 0.13691 u

Energy equivalent = 0.13691×931.50.13691 \times 931.5 MeV/c² = 127.5 MeV/c²

The energy needed to separate ¹⁶₈O into its constituents is 127.5 MeV/c².

Exercise: Example 13.3 | Q: Example 13.3 | (Page 6)
For More Understanding

Explanation

This numerical problem demonstrates Einstein's mass-energy equivalence (E = mc²). The conversion factor 1 u = 931.5 MeV/c² is a fundamental constant used throughout nuclear physics. The mass defect of oxygen-16 (0.13691 u) represents the mass 'lost' when 8 protons and 8 neutrons combine to form the nucleus, converted to energy equivalent using the established conversion factor.

Solution Steps

  1. Step 1: Calculate energy equivalent of 1 u in Joules using E = mc²

  2. Step 2: Convert Joules to MeV using electron charge conversion

  3. Step 3: Apply the conversion factor to express mass defect of oxygen-16 in MeV/c²

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