In a nuclear weapon, approximately 0.073% of the mass of a material is converted into energy. If there are 3 kgs of fissionable material in a nuclear weapon, how much energy is released? Use MJ (mega joules) as your unit
Question
In a nuclear weapon, approximately 0.073% of the mass of a material is converted into energy. If there are 3 kgs of fissionable material in a nuclear weapon, how much energy is released? Use MJ (mega joules) as your unit
Solution 1
To solve this problem, we can use Einstein's mass-energy equivalence principle, which states that E=mc^2, where E is energy, m is mass, and c is the speed of light.
First, we need to find the mass that is converted into energy. This is 0.073% of 3 kg, or 0.00073 * 3 kg = 0.00219 kg.
Next, we plug this mass into the formula E=mc^2. The speed of light c is approximately 3 * 10^8 m/s. So,
E = 0.00219 kg * (3 * 10^8 m/s)^2 = 1.9681 * 10^14 Joules.
To convert this to mega joules (MJ), we divide by 10^6:
E = 1.9681 * 10^14 J / 10^6 = 196810000 MJ.
So, approximately 196810000 MJ of energy is released.
Solution 2
To calculate the energy released, we can use Einstein's mass-energy equivalence principle, which states that E=mc^2, where E is energy, m is mass, and c is the speed of light.
First, we need to calculate the mass that is converted into energy. Given that 0.073% of the mass is converted, this is 0.073/100 * 3 kg = 0.00219 kg.
The speed of light, c, is approximately 3 * 10^8 m/s.
Substituting these values into the equation gives:
E = 0.00219 kg * (3 * 10^8 m/s)^2 E = 0.00219 kg * 9 * 10^16 m^2/s^2 E = 1.971 * 10^14 Joules
To convert this to mega joules (MJ), we divide by 10^6:
E = 1.971 * 10^14 Joules / 10^6 E = 1.971 * 10^8 MJ
So, approximately 197,100,000 MJ of energy is released.
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