Question 43.6: What Happens to Cobalt-57? The rest mass of 27^57 Co is 56.9......
What Happens to Cobalt-57?
The rest mass of _{27}^{57}Co is 56.936296 u, and the rest mass of _{26}^{57} Fe is 56.935399 u. Can _{27}^{57}Co undergo spontaneous electron capture to become _{26}^{57} Fe ? If so, how much energy is released? Give your answer in MeV to three significant figures. To keep this simple ignore the neutrino.
INTERPRET and ANTICIPATE
We need to know if the mass of the reactants is greater than or less than the mass of the products. It is helpful to write the electron capture reaction: { }_{27}^{57} Co + e ^{-} \rightarrow{ }_{26}^{57} Fe +\nu \text {. }
SOLVE
First, find the sum of the masses of the electron and { }_{27}^{57} Co. Use m_{ e }=5.48579909 \times 10^{-4} u for the electron’s mass.
Compare the mass of the reactants to that of the products.
m_{ e }+m_{ Co }>m_{ Fe }Electron capture is possible.
Find the difference in mass and multiply by c² to find the energy released.
CHECK and THINK
This released energy goes into the total energy of the neutrino and the kinetic energy of the iron. The neutrino travels outward without interacting further, but the iron can interact with other particles, sharing this energy.