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Question: A \[{{^{238}}_{92}}U\] emits \[8\alpha \] particles and \[6\beta \] particles. The neutron/ proton r...

A 23892U{{^{238}}_{92}}U emits 8α8\alpha particles and 6β6\beta particles. The neutron/ proton ratio in the product nucleus is:
(a) 60/41
(b) 61/40
(c) 62/41
(d) 61/42

Explanation

Solution

Uranium is a radioactive metal which is heavy and has a high atomic mass number. It is a radioactive substance due to its nucleus instability it emits alpha and beta particles. By emitting alpha and beta particles it becomes more stable. The given uranium has the atomic number of 92 and the mass number equal to 238.

Complete answer:
If an alpha particle has been emitted by the substance then the decrease in its mass number will be the four times the amount of alpha particles released and the decrease in its atomic number will be the two times its number of alpha particles emitted. As we know that 8 alpha particles have been emitted by uranium so the change in its mass number will be four times of eight, that is it will be decreased by 32. The change in the atomic number will be two times of eight that is sixteen so the atomic number will be decreased by 16.

Now see the following equation to understand clearly:
23892U→8αZ−8(2)XA−4(8)=Z−16XA−32{{^{238}}_{92}}U{{\xrightarrow{8\alpha }}_{Z-8(2)}}{{X}^{A-4(8)}}{{=}_{Z-16}}{{X}^{A-32}}
Now when a beta particle is emitted there is no change in the mass number but the atomic number is changed by the number of particles of beta which have been emitted. So in the uranium atom which we get when alpha particles have been emitted through it, then the mass number of that will remain the same but the atomic number will be increased by six.

Now see the following equation to understand clearly:
Z−16XA−32→6βZ−16+6(1)YA−32→Z−10YA−32_{Z-16}{{X}^{A-32}}{{\xrightarrow{6\beta }}_{Z-16+6(1)}}{{Y}^{A-32}}{{\to }_{Z-10}}{{Y}^{A-32}}
So A will be equal to =238-32= 206( mass number)
And Z will be equal to= 92-10=82( atomic number)
So to calculate the number of neutrons the formula is
= mass number – atomic number (A-Z)
= 206 - 82
= 124
And the number of protons is equal to the atomic number so it is equal to 82
Now the neutron/ proton ratio will be = np=12482=6241\dfrac{n}{p}=\dfrac{124}{82}=\dfrac{62}{41}
So the correct option is, ‘(c) 62/41’.

Note: Uranium tends to form many isotopes. The pure form of uranium tends to have silver colour which has the ability to get oxidise in air. uranium fission is made efficient by nuclear engineers. Uranium has a name named after the planet Uranus.