Question

How many α and β-particles are emitted in the transmutation \[\ce{^232_90Th -> ^208_82Pb}\]?

Answer 1

\[\ce{^232_90Th -> ^208_82Pb}\]

The emission of one α-particle decreases the mass number by 4 whereas the emission of β-particles has no effect on the mass number.

Net decrease in mass number = 232 - 208 = 24.

This decrease is only due to α-particles. Hence, number of α-particles emitted = `24/4 = 6`

Now, the emission of one α-particle decreases the atomic number by 2 and one β-particle emission increases it by 1.

The net decrease in atomic number = 90 - 82 = 8

The emission of 6 α-particles causes a decrease in atomic number by 12. However, the actual decrease is only 8.

Thus, the atomic number increases by 4. This increase is due to the emission of 4 β-particles.

Thus, 6 α and 4 β-particles are emitted.