Question

Calculate N-Z ratio for Xe-135 and predict the type of decay it will undergo?

I understand how to get the ratio, which is 1.5. However, how do I predict the type of decay?

Answer 1

The `N:Z` ratio is 1.50; the nucleus will undergo β-decay.

Explanation:

`""_54^135"Xe"` has 54 protons and 135-54 = 81 neutrons.

Thus, `N:Z = 81:54 = 1.50`

Nuclei have a Belt of Stability, that is, a range of `N:Z` ratios within which they are stable.

(Adapted from ... http://www.kentchemistry.com/links/Nuclear/BandStability.)

The red dot on the diagram above shows the position of `""_54^135"Xe"` .

The range of stability for xenon nuclei is 1.30 to 1.48. The value of 1.50 for `""_54^135"Xe"` is just outside this range and in the blue area of the diagram.

A high `"N:Z` ratio (the blue area of the diagram) tells you that the nucleus has too many neutrons (or too few protons) to be stable.

A neutron spontaneously changes to a proton and emits an electron (a β particle).

Thus the nucleus undergoes β-decay.

The equation for the transformation is

`""_54^135"Xe" → ""_55^135"Cs" + ""_text(-1)^0"e"`