Q.142 Physics ⭐ 360° Option Elimination Active

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NEET 2020 Physics Question 142 Solution

Topic: Nuclei · Official NTA Booklet Code E1

Question

The energy equivalent of 0.5 g of a substance is:

✓

Verified Against NTA Final Answer Key

Option (2) : 4.5×1013 J

📚 Nuclei Easy

📋 Given Parameters & Problem Setup

Mass (m) 0.5 g = 0.5 × 10^-3 kg = 5 × 10^-4 kg

Speed of Light (c) 3 × 10^8 m s^-1

Equation E = m c^2

Question Objective Calculate the equivalent energy in Joules

⚡

The 30-Second Exam Hall Shortcut: ⚡ "E = mc^2 = (0.5 × 10^-3 kg) × (3 × 10^8 m/s)^2 = 0.5 × 9 × 10^13 = 4.5 × 10^13 J!"

⏱️ 15 seconds

Convert mass to SI units: $m = 0.5\text{ g} = 0.5 \times 10^{-3}\text{ kg}$ . Speed of light $c = 3 \times 10^8\text{ m/s}$ , so $c^2 = 9 \times 10^{16}\text{ m}^2/\text{s}^2$ . Energy $E = mc^2 = (0.5 \times 10^{-3}) \times (9 \times 10^{16}) = 4.5 \times 10^{13}\text{ J}$ . Mark Option (2) in 5 seconds!

1 Formula: E = m c^2.

2 Convert mass to kg: m = 0.5 g = 0.5 × 10^-3 kg.

3 Square speed of light: c^2 = (3 × 10^8)^2 = 9 × 10^16 m^2/s^2.

4 Multiply: E = 0.5 × 10^-3 × 9 × 10^16 = 4.5 × 10^13 J.

5 Option (1) has power 10^16 (forgot to convert grams to kg).

6 Select Option (2) 4.5 × 10^13 J.

🛡️

Why You Can 100% Trust This Shortcut: NCERT Physics · Nuclei (Mass-Energy and Nuclear Binding Energy: Einstein's Relation)

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Einstein's Mass-Energy Equivalence Principle

Einstein showed that mass is another form of energy and that mass and energy can be converted into each other according to the famous relation: $E = m c^2$ where $m$ is mass in kilograms and $c$ is the speed of light in vacuum in meters per second.

Step 2

Convert Mass into Standard SI Units (kg)

Given mass in grams: $m = 0.5\text{ g} = 0.5 \times 10^{-3}\text{ kg} = 5.0 \times 10^{-4}\text{ kg}$

Step 3

Substitute into Mass-Energy Equation

Using the standard value for the speed of light $c = 3.0 \times 10^8\text{ m s}^{-1}$ : $c^2 = (3.0 \times 10^8)^2 = 9.0 \times 10^{16}\text{ m}^2\text{ s}^{-2}$ $E = (0.5 \times 10^{-3}\text{ kg}) \times (9.0 \times 10^{16}\text{ m}^2\text{ s}^{-2})$ $E = 4.5 \times 10^{13}\text{ Joules (J)}$

Step 4

Verify Physical Magnitude

This is an enormous release of energy ( $4.5 \times 10^{13}\text{ J}$ , equivalent to about 10 kilotons of TNT) released from merely half a gram of annihilated matter.

⭐

360° Option Elimination Engine Key Feature

Diagnose every choice: Know exactly why the right option works and why distractors fail.

4-Option Deep Scan

1 A

✗ Incorrect

Verdict & Scientific Reason:

Incorrect; classic unit trap resulting from failing to convert grams ( $0.5\text{ g}$ ) into kilograms ( $10^{-3}\text{ kg}$ ).

⚠️

Student Fallacy (Why candidates pick this trap): Plugging in mass as 0.5 without converting to kilograms.

2 B

✓ 100% Correct

Verdict & Scientific Reason:

Factually and mathematically exact; $0.5 \times 10^{-3} \times 9 \times 10^{16} = 4.5 \times 10^{13}\text{ J}$ .

💡

Why this is airtight: None; clean SI conversion and calculation.

3 C

✗ Incorrect

Verdict & Scientific Reason:

Incorrect; arithmetic error of multiplying by $c$ instead of $c^2$ ( $0.5 \times 3 = 1.5$ ).

⚠️

Student Fallacy (Why candidates pick this trap): Using

E = mc

instead of

E = mc^2

4 D

✗ Incorrect

Verdict & Scientific Reason:

Incorrect; forgetting to multiply by the factor of 9 from $3^2$ .

⚠️

Student Fallacy (Why candidates pick this trap): Ignoring the 9 in

c^2

⚠️

NTA Trap Alert: Gram to Kilogram Conversion Trap

Never forget to convert grams to kilograms in $E = mc^2$ ! $1\text{ g} = 10^{-3}\text{ kg}$ . If you forget, you get $4.5 \times 10^{16}\text{ J}$ (Option 1, the distractor!).

🛡️ How to avoid the -1 mark: Always convert grams to kilograms first: 0.5 g = 0.5 × 10^-3 kg!

📖

Core NEET Syllabus Standard

Physics · Nuclei Standard Benchmark

Core Scientific Principle Tested:

Syllabus Focus: Einstein's Mass-Energy Equivalence: E = mc^2 Calculation

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

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NEET 2020 Physics Question 142 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ "E = mc^2 = (0.5 × 10^-3 kg) × (3 × 10^8 m/s)^2 = 0.5 × 9 × 10^13 = 4.5 × 10^13 J!"

Step-by-Step Rigorous Workflow & Mathematical Proof

Einstein's Mass-Energy Equivalence Principle

Convert Mass into Standard SI Units (kg)

Substitute into Mass-Energy Equation

Verify Physical Magnitude

360° Option Elimination Engine Key Feature

NTA Trap Alert: Gram to Kilogram Conversion Trap

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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