Some nucleus of 74X189 (atomic mass = 188.96191 u) undergoes - decay to become 75X189 (atomic mass = 188.95922 u). What is the energy (in MeV) released in this process?
To calculate the energy released in this process, we need to use Einstein's famous equation, E = mc^2, where E represents the energy, m represents the mass difference, and c is the speed of light (approximately 3 x 10^8 m/s).
1. Calculate the mass difference (Δm):
Δm = mass of the initial nucleus - mass of the final nucleus
Δm = 188.96191 u - 188.95922 u
Δm = 0.00269 u
2. Convert the mass difference from atomic mass units (u) to kilograms (kg):
Mass in kg = mass in u x 1.66054 x 10^-27 kg/u
Δm = 0.00269 u x 1.66054 x 10^-27 kg/u
Δm = 4.461 x 10^-30 kg
3. Calculate the energy (E) using E = mc^2:
E = Δm x c^2
E = 4.461 x 10^-30 kg x (3 x 10^8 m/s)^2
4. Convert the energy from joules (J) to megaelectronvolts (MeV):
1 MeV = 1.60218 x 10^-13 J
E = E / (1.60218 x 10^-13 J/MeV)
E = (4.461 x 10^-30 kg x (3 x 10^8 m/s)^2) / (1.60218 x 10^-13 J/MeV)
Calculating this gives us the energy released in MeV.