How much energy is released in the beta decay of 14 C?
Since carbon-14 decays into Nitrogen-14,
the mass of carbon 14 is 14.003242 and the mass of nitrogen 14 is 14.003074, What I did was:
(14.003242-14.003074)u * 931.5 MeV/c^2 = (0.156 MeV/c^2)*c^2 = .156 MeV
but that's not the answer, am I doint something wrong?
Did you include the rest energy of the electron emitted in the beta decay process?
You can neglect the neutrino rest mass energy, since its mass is nearly zero. It does carry significant momentum.
You are right, considering the mass of the electron emitted I got .352 MeV, which is the correct answer. Everywhere I looked on the internet said to neglect this mass, but I guess it does make a difference. My answer was negative though, does that mean that I only consider the absolute value of whatever I get?
I guess the answer is 0.157 MeV.
Your approach to calculate the energy released in the beta decay of carbon-14 is correct. However, there might be a small rounding error in your calculations that resulted in a slightly different answer. Let's go through the calculation step by step to determine the exact value.
The equation you used to calculate the energy released in beta decay is:
Energy = (Mass of parent nucleus - Mass of daughter nucleus) × (speed of light)^2
The atomic mass unit (u) is approximately equal to 931.5 MeV/c^2.
1. First, calculate the mass difference between carbon-14 and nitrogen-14:
Mass difference = (14.003242 u - 14.003074 u) = 0.000168 u
2. Convert the mass difference into energy:
Energy = (0.000168 u) × (931.5 MeV/c^2)
Energy = 0.156648 MeV
So the energy released in the beta decay of carbon-14 is approximately 0.157 MeV. It seems that your initial estimate had a rounding error.