To calculate the energy released in a nuclear reaction, you can use Einstein's famous equation, E = mc², where E is the energy released, m is the change in mass, and c is the speed of light (approximately 3.0 x 10^8 meters per second).
First, we need to calculate the change in mass (∆m) in kilograms.
Given: Mass of reactant (m₁) = 236.05 a.m.u Mass of product (m₂) = 253.86 a.m.u 1 a.m.u = 1.667x10^-27 kg
Converting the masses to kilograms: m₁ = 236.05 a.m.u x 1.667x10^-27 kg/a.m.u m₂ = 253.86 a.m.u x 1.667x10^-27 kg/a.m.u
Next, calculate the change in mass (∆m): ∆m = m₂ - m₁
Now, we can calculate the energy released (E): E = ∆m * c²
Using the given value for the speed of light (c = 3.0 x 10^8 m/s), we can substitute the values and calculate the energy released.
Here's the step-by-step calculation:
m₁ = 236.05 a.m.u x 1.667x10^-27 kg/a.m.u ≈ 3.9321x10^-25 kg
m₂ = 253.86 a.m.u x 1.667x10^-27 kg/a.m.u ≈ 4.2296x10^-25 kg
∆m = m₂ - m₁ ≈ 4.2296x10^-25 kg - 3.9321x10^-25 kg ≈ 2.9745x10^-26 kg
E = ∆m * c² ≈ 2.9745x10^-26 kg * (3.0 x 10^8 m/s)² ≈ 2.9745x10^-26 kg * 9.0 x 10^16 m²/s² ≈ 2.67705x10^-9 J
Therefore, the energy released in the nuclear reaction is approximately 2.67705x10^-9 joules (J).