Question

What is the electron capture reaction for astatine-200 in terms of the individual steps?

Answer 1

Electron capture is when an inner-core electron (`""_(-1)^(0) e`) combines with a proton (`""_1^1 p`) in a nucleus to spit out a neutron (`""_(0)^(1) n`) and a neutrino (a neutral fermion, denoted `nu`):

`""_(-1)^(0) e + ""_1^1 p -> ""_(0)^(1) n`

A neutron can then combine into an isotope to give:

`""_(Z)^(A) X + ""_(0)^(1) n -> ""_(Z)^(A+1) X`

And a proton that was used up in the process is lost as follows:

`""_(Z)^(A+1) X -> ""_(Z-1)^(A) X + ""_(1)^(1) p`

Astatine-200, `"At"-200`, has atomic number `Z = 85` and mass number `A = 200`, so its isotope notation is:

`""_(85)^(200) "At"`

So, this isotope takes in an electron to lose a proton and gain a neutron as described above:

`""_(-1)^(0) e + cancel(""_1^1 p) -> cancel(""_(0)^(1) n)`

`""_(85)^(200) "At" + cancel(""_(0)^(1) n) -> cancel(""_(85)^(201) "At")`

`cancel(""_(85)^(201) "At") -> ""_(84)^(200) "Po" + cancel(""_(1)^(1) p) + nu`

Overall, we then get...

`color(blue)ul(""_(85)^(200) "At" + ""_(-1)^(0) e -> ""_(84)^(200) "Po" + nu)`

And with `Z = 84`, the element becomes a polonium-200 isotope.