Use the table to the right to answer the following question.
How many kilograms of isotope would be required to supply the energy needs of country Upper B for 1​ year?
Item
Energy​ (joules)
Energy released by burning 1 kg of a certain combustible sedimentary rock
1.6 times 10 Superscript 9
Energy released by fission of 1 kg of a certain isotope
5.6 times 10 Superscript 13
Energy released by fusion of hydrogen in 1 liter of water
7 times 10 Superscript 13
Country A annual energy consumption
3 times 10 Superscript 20
Country B annual energy consumption
5 times 10 Superscript 19
Question content area bottom
Part 1
It would take approximately

enter your response here kilograms.

To determine how many kilograms of the isotope would be required to supply the energy needs of Country B for one year, we can use the given information.

### Step 1: Identify the relevant data
- Energy released by fission of 1 kg of the isotope: \( 5.6 \times 10^{13} \) joules.
- Country B's annual energy consumption: \( 5 \times 10^{19} \) joules.

### Step 2: Set up the equation
Let \( x \) be the number of kilograms of the isotope needed. The total energy provided by \( x \) kilograms of the isotope can be expressed as:
\[
\text{Total energy} = x \times \left( 5.6 \times 10^{13} \text{ joules} \right)
\]

We want this total energy to equal Country B's annual energy consumption:
\[
x \times \left( 5.6 \times 10^{13} \right) = 5 \times 10^{19} 
\]

### Step 3: Solve for \( x \)
\[
x = \frac{5 \times 10^{19}}{5.6 \times 10^{13}}
\]

### Step 4: Perform the calculation
\[
x = \frac{5}{5.6} \times \frac{10^{19}}{10^{13}} = \frac{5}{5.6} \times 10^{6}
\]
\[
x \approx 0.892857 \times 10^{6} \approx 8.93 \times 10^{5} \text{ kg}
\]

So, it would take approximately **\( 8.93 \times 10^{5} \) kilograms** of the isotope to supply the energy needs of Country B for one year.

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Would you like further details or have any questions? 

Here are some related questions to explore:
1. How does the energy released by fission compare to that of fusion?
2. What would be the required mass of the isotope for Country A's energy needs?
3. How much more energy does fusion provide compared to the combustion of sedimentary rock?
4. What are the environmental implications of using isotopes for energy?
5. How do the energy needs of Country A and Country B compare in terms of resource usage?

**Tip:** Always check the units to ensure that you're performing the calculation correctly.

Learn how to calculate the mass of an isotope required to meet Country B's annual energy needs using energy conversion formulas. Detailed solution provided for the mathematical problem involving energy release by fission and annual energy consumption.

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