Question

Complete the following nuclear changes:
$a\left)AZX\stackrel{\alpha }{\to }{X}_1\stackrel{\gamma }{\to }{X}_2\stackrel{2\beta }{\to }{X}_{3}b\right)X\stackrel{\beta }{\to }{X}_1\stackrel{\alpha }{\to }{X}_2\stackrel{\alpha }{\to }17269X_3$

Answer 1

a) Firstly, parent nucleus X changes into daughter nucleus $X_1$ due to alpha decay. When an alpha particle is emitted, atomic and mass number are decreased by 2 and 4 respectively.

$AZX\to A-4Z-2X_1+42\alpha$

Secondly, parent nucleus $X_1$ changes into daughter nucleus $X_2$ due to gamma decay. When a gamma particle is emitted, both, atomic number and mass number remain unchanged.

$A-4Z-2X1\to A-4Z-2X_2+00\gamma$

Later, parent nucleus $X_2$ changes into daughter nucleus $X_3$ due to double beta decay. When a beta particle emits, mass number of the parent nucleus remains the same but atomic number increases by one unit.

$A-4Z-2X2\to A-4zX3+20-1\beta$

Complete nuclear reaction is:

$AZX\to A-4Z-2X1\to A-4Z-2X2\to A-4Z{X}_3$



b) Let the atomic number and atomic mass of the parent nucleus are Z and A. First parent nucleus X changes into daughter nucleus $X_1$ due to beta decay. When a beta particle emits, mass number of the parent nucleus remains the same but atomic number increases by one unit.

$AZX\to AZ+1X1+0-1\beta$

Now, parent nucleus $X_1$ changes into daughter nucleus $X_2$ due to alpha decay. When an alpha particle is emitted, atomic and mass number are decreased by 2 and 4 respectively.

$AZ+1X1\to A-4Z-1X2+42\alpha$

Again, parent nucleus $X_2$ changes into daughter nucleus $X_3$ due to alpha decay. When an alpha particle is emitted, atomic and mass number are decreased by 2 and 4 respectively.

$A-4Z-1X2\to A-8Z-3X3+42\alpha$

Compare $A-8Z-3X3$ with daughter nucleus $17269X3$

Therefore,
Z - 3 = 69 and A - 8 = 172
We get, Z = 72, and A = 180

Final reaction is:

$18072X\to 18073X_1\to 17671X_2\to 17969X_3$