Question 2 of 13beginner🔧 ApplyNumerical2 marks

Calculate the energy equivalent of 1 g of substance.

Correct Answer

Given: Mass, m = 1 g = 10⁻³ kg

Formula: Using Einstein's mass-energy equivalence relation: E = mc²

Calculation: E = 10⁻³ × (3×103 \times 10⁸)² J E = 10⁻³ × 9×109 \times 10¹⁶ J E = 9×109 \times 10¹³ J

Thus, if one gram of matter is converted to energy, there is a release of enormous amount of energy.

Exercise: Example 13.2 | Q: Example 13.2 | (Page 5)
For More Understanding

Explanation

This is a direct application of Einstein's mass-energy equivalence relation E = mc² from Section 13.4.1 of the textbook. The mass of 1 gram is converted to SI units (10⁻³ kg), and the speed of light c is taken as 3×103 \times 10⁸ m/s. The calculation shows that even a small mass of 1 gram corresponds to a huge energy of 9×109 \times 10¹³ joules, demonstrating the enormous energy potential locked in matter.

Solution Steps

  1. Step 1: Convert mass from grams to kilograms: m = 1 g = 10⁻³ kg

  2. Step 2: Apply Einstein's mass-energy relation: E = mc²

  3. Step 3: Substitute values: E = 10⁻³ × (3×103 \times 10⁸)² J

  4. Step 4: Calculate: E = 10⁻³ × 9×109 \times 10¹⁶ = 9×109 \times 10¹³ J

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