Physics Class 12 NCERT Solutions: Chapter 13 Nuclei Part 6

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Q value of Beta decay

Q Value of Beta Decay

Q: 14. The nucleus decays by emission. Write down the decay equation and determine the maximum kinetic energy of the electrons emitted. Given that:

Answer:

In emission, the number of protons increases by, and one electron and an antineutrino are emitted from the parent nucleus.

Emission of the nucleus is given as:

It is given that:

Atomic mass of

Atomic mass of

Mass of an electron,

Q-value of the given reaction is given as:

There are electrons in and electrons in . Hence, the mass of the electron is cancelled in the Q-value equation.

The daughter nucleus is too heavy as compared to. Hence, it carries negligible energy. The kinetic energy of the antineutrino is nearly zero. Hence, the maximum kinetic energy of the emitted electrons is almost equal to the Q-value, i.e..

Q: 15. The Q value of a nuclear reaction is defined by where the masses refer to the respective nuclei. Determine from the given data the value of the following reactions and state whether the reactions are exothermic or endothermic.

(i)

(ii)

Atomic masses are given to be

Answer:

(i) The given nuclear reaction is:

It is given that:

Atomic mass

Atomic mass

Atomic mass

According to the question, the Q-value of the reaction can be written as:

But

The negative Q-value of the reaction shows that the reaction is endothermic.

(ii) The given nuclear reaction is:

It is given that:

Atomic mass of

Atomic mass of

Atomic mass of

The Q-value of this reaction is given as:

The positive Q-value of the reaction shows that the reaction is exothermic.

Q: 16. Suppose, we think of fission of a nucleus into two equal fragments, . Is the fission energetically possible Argue by working out of the process. Given and.

Answer:

The fission of can be given as:

It is given that:

Atomic mass of

Atomic mass of

The Q-value of this nuclear reaction is given as:

But

The Q-value of the fission is negative. Therefore, the fission is not possible energetically. For an energetically - possible fission reaction, the Q-value must be positive.

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