Question

A plutonium atom undergoes nuclear fission. Identify the missing element in the nuclear equation.

230 pu

Answer 1

`_(92)^(226)U`

Step-by-step explanation:

Let's firstly identify the atomic number (the number of protons) of Pu. This is done by referring to the periodic table and finding Pu. The atomic number of Pu is:

`Z=94`

In order to identify the type of a nuclear decay, we need to find the N/Z ratio. This is the ratio between the number of neutrons and the atomic number of an isotope. The number of neutrons is found by subtracting the number of protons from the mass number:

`N=M-Z`

That said, the N/Z ratio equation becomes:

`N/Z=(M-Z)/(Z)=(M)/(Z)-1=(230)/(94)-1=1.45`

This is a relatively high number thinking about the belt of stability of isotopes. Ideally, stable isotopes with a low Z value have an N/Z ratio of 1. Heavier isotopes with Z > 50 would have a slightly higher N/Z ratio and would be stable around N/Z = 1.25. This means we wish to decrease the N/Z ratio as much as possible.

Among all the decays, alpha-decay is preferred to decrease the N/Z ratio significantly (1.45 is much higher than 1.25). That said, we'll release an alpha particle with some nucleotide X of mass M and atomic number Z:

`_(94)^(230)Pu\rightarrow _Z^MX+_2^4\alpha`

According to the mass and charge conservation law:

`230=M+4\therefore M=230 - 4 = 226`

`94=Z+2\therefore Z = 94-2 = 92`

Identify an element with Z = 92 in the periodic table. This is uranium, U:

`_(92)^(226)U`