Questions: One of the most famous equations is Einstein's E=mc^2. If you could somehow change the mass of a 1.0-gram paper clip into paper clip into pure energy, how many joules of energy would result? (Hint: 1,000 grams =1 kg ) From your answer from part 1, convert this into tons of TNT. The ton of TNT is a unit of energy defined to be 4.184 gigajoules or 4.184 x 10^9 joules. How does this compare to a modern-day atomic bomb?

One of the most famous equations is Einstein's E=mc^2. If you could somehow change the mass of a 1.0-gram paper clip into paper clip into pure energy, how many joules of energy would result? (Hint: 1,000 grams =1 kg ) From your answer from part 1, convert this into tons of TNT. The ton of TNT is a unit of energy defined to be 4.184 gigajoules or 4.184 x 10^9 joules. How does this compare to a modern-day atomic bomb?
Transcript text: One of the most famous equations is Einstein's $E=m c^{2}$. If you could somehow change the mass of a 1.0-gram paper clip into paper clip into pure energy, how many joules of energy would result? (Hint: 1,000 grams $=1 \mathrm{~kg}$ ) From your answer from part 1 , convert this into tons of TNT. The ton of TNT is a unit of energy defined to be 4.184 gigajoules or $4.184 \times 10^{9}$ joules. How does this compare to a modern-day atomic bomb?
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Solution

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Solution Steps

Step 1: Calculate the Energy from Mass using \(E = mc^2\)

First, we need to convert the mass of the paper clip from grams to kilograms: \[ 1.0 \, \text{gram} = 0.001 \, \text{kg} \]

Next, we use Einstein's equation \(E = mc^2\) to find the energy: \[ E = (0.001 \, \text{kg}) \times (3.00 \times 10^8 \, \text{m/s})^2 \]

Calculating the energy: \[ E = 0.001 \times (9.00 \times 10^{16}) \] \[ E = 9.00 \times 10^{13} \, \text{joules} \]

Step 2: Convert Energy to Tons of TNT

We know that 1 ton of TNT is equivalent to \(4.184 \times 10^9\) joules. To convert the energy from joules to tons of TNT: \[ \text{Energy in tons of TNT} = \frac{9.00 \times 10^{13} \, \text{joules}}{4.184 \times 10^9 \, \text{joules/ton}} \]

Calculating the energy in tons of TNT: \[ \text{Energy in tons of TNT} = \frac{9.00 \times 10^{13}}{4.184 \times 10^9} \] \[ \text{Energy in tons of TNT} \approx 2.151 \times 10^4 \, \text{tons of TNT} \]

Final Answer

  1. The energy resulting from converting the mass of a 1.0-gram paper clip into pure energy is: \[ \boxed{9.00 \times 10^{13} \, \text{joules}} \]

  2. The energy in tons of TNT is: \[ \boxed{2.151 \times 10^4 \, \text{tons of TNT}} \]

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