A material contains a radioactive isotope that disintegrates solely by the emission of α-particles at a rate of 100 s-1.

Question 1

A material contains a radioactive isotope that disintegrates solely by the emission of α-particles at a rate of 100 s^-1.

Which statement about this material is correct?

A The number of atoms in the material diminishes at a rate of 100 s^-1.

B The number of neutrons in the material diminishes at a rate of 100 s^-1.

C The number of nucleons in the material diminishes at a rate of 400 s^-1.

D The number of protons in the material diminishes at a rate of 100 s^-1.

Reference: Past Exam Paper – November 2012 Paper 12 Q39

Solution 1:

Answer: C.

A nucleon is either a proton or a neutron.

An α-particle is a helium nucleus; with nucleon number 4 and proton number 2. So, each α-decay reduces the number of nucleons in the material by 4, but does not change the number of atoms.

An atom consists of protons and neutrons, that is, an atoms consists of nucleons. Thus, during emission of α-particles, the number of nucleon decreases, but not the number of atoms. [A incorrect]

This material disintegrates by emitting 100 α-particles per second.

With a decay of an alpha particle, 2 neutrons + 2 protons are emitted. So the number of neutrons and protons in the material each diminishes at a rate of 200s^-1 as 100 particles are emitted per second. [B and D incorrect]

The total number of nucleons (protons + neutrons) in the material diminishes at a rate of 400s^-1.