In a nuclear reaction, the mass defect is 2 x \(10^{-6}\)g. Calculate the energy released given that the velocity of light is 3 x \(10^{8}ms^{-1}\)
Question 1 Report
In a nuclear reaction, the mass defect is 2 x \(10^{-6}\)g. Calculate the energy released given that the velocity of light is 3 x \(10^{8}ms^{-1}\)
Answer Details
When a nuclear reaction takes place, the total mass of the reactants may not be equal to the total mass of the products due to the conversion of some mass into energy. This is because mass and energy are interchangeable according to the famous equation E=mc², where E is energy, m is mass, and c is the speed of light. The mass defect is the difference between the total mass of the reactants and the total mass of the products, and it represents the mass that has been converted into energy.
To calculate the energy released, we can use the equation E=mc², where m is the mass defect. We can convert the mass defect from grams to kilograms by dividing by 1000:
mass defect = 2 x \(10^{-6}\) g = 2 x \(10^{-9}\) kg
The speed of light is 3 x \(10^{8}ms^{-1}\). Substituting these values into the equation, we get:
E = (2 x \(10^{-9}\) kg) x (3 x \(10^{8}ms^{-1}\))² = 1.8 x \(10^{8}\) J
Therefore, the energy released in the nuclear reaction is 1.8 x \(10^{8}\) J.
The correct option is: 1.8 x \(10^{8}\) J
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