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YOUR PARTICIPATION FOR THE GROWTH OF PHYSICS REFERENCE BLOG

Tuesday, August 21, 2018

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.

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