Question

In the fission process

$\mathbf{235}\mathbf{U}\mathbf{+}\mathbf{n}{\mathbf{\to }}^{\mathbf{132}}\mathbf{}\mathbf{Sn}\mathbf{+}{}_{\boxed{\mathbf{\colon\colon }}}{}^{\boxed{\mathbf{\colon\colon }}}\mathbf{}\boxed{\mathbf{\colon\colon }}\mathbf{+}\mathbf{3}\mathbf{}\mathbf{n}$

what number goes in (a) the elevated box (the superscript) and (b) the descended box (the value of Z)?

Short answer

(a) The mass number of an unknown atom is 101.

(b) The atomic number of an unknown atom is 42.

Step-by-step solution

Identification of given data

The mass number of Uranium is${\mathrm{A}}_1=235$

The number of attacking neutrons before fission is ${\mathrm{n}}_{1}1$

The mass number of the Tin is ${\mathrm{A}}_2=132$

The number of attacking neutrons before fission is ${\mathrm{n}}_2=3$

Radioactive decay is the process of decaying of protons from the nucleus and variation in the mass number of the atom. The number of protons increases by one unit due to beta decay and no change in the mass number of the atom, while the number of protons changes by two units and mass number by four units for alpha decay.

Determination of the mass number of unknown atom(a)

The mass number of the unknown atom is given as:

${\mathrm{A}}_1+{\mathrm{n}}_1={\mathrm{A}}_2+{\mathrm{A}}_3+{\mathrm{n}}_2$

Substitute all the values in the above equation.

role="math" localid="1661601308977" $$\begin{gathered} 235+1=132+{\mathrm{A}}_3+{\mathrm{n}}_2 \\ {\mathrm{A}}_3=101 \end{gathered}$$

Therefore, the mass number of an unknown atom is 101

Determination of the atomic number of unknown atom(b)

The atomic number of an unknown atom is calculated as:

${\mathrm{Z}}_3={\mathrm{Z}}_1-{\mathrm{Z}}_2$

Here, ${\mathrm{Z}}_1$and ${\mathrm{Z}}_2$are the atomic numbers of Uranium and Tin. The values of these numbers are 92 and 50.

Substitute all the values in the above equation.

$$\begin{gathered} {\mathrm{Z}}_3=92-50 \\ =42 \end{gathered}$$

Therefore, the atomic number of an unknown atom is 42 .