The nucleus `""_10^23"Ne"` decays by `beta^(-)`emission. Write down the β decay equation and determine the maximum kinetic energy of the electrons emitted. Given that:

`"m"(""_10^23 "Ne")` = 22.994466 u

`"m"(""_11^23 "Na")` = 22.989770 u.

#### Solution

In `beta^(-)` emission, the number of protons increases by 1, and one electron and an antineutrino are emitted from the parent nucleus.

`beta^(-)` emission of the nucleus `""_10^23"Ne"` is given as:

\[\ce{^23_10 Ne -> ^23_11Na + e- + \bar{v} + Q}\]

It is given that:

Atomic mass of ,`"m"(""_10^23 "Ne")`= 22.994466 u

Atomic mass of `"m"(""_11^23 "Na")` = 22.989770 u

Mass of an electron, m_{e }= 0.000548 u

Q-value of the given reaction is given as:

`"Q" = ["m"(""_10^23"Ne") - ["m"(""_11^23 "Na") + "m"_"e")]]"c"^2`

There are 10 electrons in `""_10^23"Ne"` and 11 electrons in . Hence, the mass of the electron is cancelled in the Q-value equation.

`therefore "Q" = [22.994466 - 22.989770]"c"^2`

`= (0.004696 "c"^2)"u"`

But 1 u = 931.5 MeV/c^{2}

`therefore "Q" = 0.004696 xx 931.5 = 4.374 "MeV"`

The daughter nucleus is too heavy as compared to `"e"^(-)` and `bar"v"`. Hence, it carries negligible energy. The kinetic energy of the antineutrino is nearly zero. Hence, the maximum kinetic energy of the emitted electrons is almost equal to the Q-value, i.e., 4.374 MeV.