Question

# Sodium-24, a radioactive isotope used medically in blood studies, decays beta decay and has a half-life of 15.0 hours. What is the product of the radioactive decay of Na-24?a. F-20b. Ne-24c. Ne-23d. Na-23e. Mg-24

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Hint:
It is seen that if a parent radioactive nucleus undergoes a beta decay, the daughter nucleus has the same mass number, but its atomic number increases by one unit.

- There are beta rays present that consist of electrons. During the conversion of a neutron into a proton, an electron is ejected out.
- Along with the electron, a particle called anti-neutrino $\overline{\nu }$ which possesses negligible mass but has a spin is also found to be emitted.
-Thus, $n\to p+{{\beta }^{-}}+\overline{\nu }$
- The change can be represented as:
${}_{11}^{24}Na\to {}_{12}^{24}Mg+{{\beta }^{-}}+\overline{\nu }$
- Atomic number of sodium is 11, thus in the periodic table, its next neighbour is magnesium, whose atomic number is 12.
-Thus, we can see here that the atomic number of daughter (which is different from that of parent) is more than that of parent by one unit, the mass number here is two, however, are the same.
- Identically, we can see that the daughter and nuclei are isobars. Isobars are those nuclei of neighbouring elements that have the same mass number. They however differ in atomic numbers and hence in number of neutrons also.

Thus we can conclude that option (e) or Mg-24 is correct.

Note:
- One should not get confused in between $\alpha$ decay and $\beta$ decay. In $\alpha$ decay the product formed was an element whose atomic and mass numbers are less than that of parent by 2 units and 4 units, respectively.
- Whereas, in$\beta$ decay we have seen that the atomic number of a daughter is more than that of a parent by one unit, the mass number of both are however the same.