A nucleus X decays into a nucleus Y by emitting an alpha particle followed by two beta particles.

Question 5

A nucleus X decays into a nucleus Y by emitting an alpha particle followed by two beta particles.

Which statement about this nuclear decay is correct?

A Beta particle decay occurs when a proton changes into a neutron.

B Nucleus Y has the same nucleon number as nucleus X.

C Nucleus Y is an isotope of nucleus X.

D The total mass of the products is equal to the mass of the initial nucleus X.

Reference: Past Exam Paper – June 2014 Paper 12 Q38

Solution:

Answer: C.

From the information give, the decay can be represented as:

X         - - - >   Y         +          ⁴₂α        +          2 ⁰_-1β

Consider option A: Beta particle decay occurs when a proton changes into a neutron.

¹₁p        - - - >   ¹₀n        +          ⁰_-1β

Beta particle has a negative charge.

Considering the charges:

Left-hand side: charge = +1               Right-hand side: charge = 0 + -1 = -1

This is incorrect as charge is not conserved.

Consider option B: Nucleus Y has the same nucleon number as nucleus X.

Let the nucleon number of nucleus Y be y and nucleon number of nucleus X be x.

Beta emission does not change the nucleon number.

Consider the nucleon number:

x = y + 4 + 2(0)

x = y + 4

y = x – 4

So, x is not equal to y.

Consider option C: Nucleus Y is an isotope of nucleus X.

Isotopes of an element are nuclei having the same proton number.

X         - - - >   Y         +          ⁴₂α        +          2 ⁰_-1β

Considering the proton numbers:

X = Y + 2 + 2(-1)

X = Y

This is correct as there is no overall change in the proton number.

Consider option D: The total mass of the products is equal to the mass of the initial nucleus X.

For any nuclear reaction / decay, there should be a mass defect which results in the release of energy.

So, the total mass is not conserved as some of it is converted into energy. However, mass-energy is conserved.