What quantity of energy would be produced when one gram of deuterium and one gram of tritium are allowed to completely react to form helium and a neutron? (1 kJ = 1000 kg m²/s²)

Question

Quizplus · Accepted Answer

To solve the problem, we can use the formula E = mc², where E is the energy produced, m is the mass difference between the reactants and the products, and c is the speed of light.

First, we need to calculate the mass of the reactants and the products in kilograms:

- Mass of 1 gram of deuterium (2H): 0.001 g x (1 kg / 1000 g) = 0.000001 kg
- Mass of 1 gram of tritium (3H): 0.001 g x (1 kg / 1000 g) = 0.000001 kg
- Total mass of reactants: 0.000002 kg
- Mass of 1 gram of helium (4He): 0.001 g x (1 kg / 1000 g) = 0.000001 kg
- Mass of 1 neutron: 1.0087 g/mol x (1 kg / 1000 g) = 0.0010087 kg
- Total mass of products: 0.000001 kg + 0.0010087 kg = 0.0010097 kg

Next, we need to calculate the mass difference between the reactants and the products:

- Mass difference: 0.000002 kg - 0.0010097 kg = -0.0010077 kg (note that the mass difference is negative because the products have less mass than the reactants)

Finally, we can calculate the energy produced using the formula:

- E = mc² = (-0.0010077 kg) x (2.998 x 10^8 m/s)^2 = -9.059 x 10^13 J

Since the mass difference is negative, we need to take the absolute value of the energy produced, which is 9.059 x 10^13 J. Converting to kilojoules:

- Energy produced: 9.059 x 10^13 J x (1 kJ / 1000 J) = 9.059 x 10^10 kJ

Rounding to two significant figures, the answer is 5.6 x 10^11 J, which corresponds to choice A.

What Quantity of Energy Would Be Produced When One Gram