# Physics Class 12 NCERT Solutions: Chapter 13 Nuclei Part 11

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Q: 27. Consider the fission of by fast neutrons. In one fission event, no neutrons are emitted and the final end products, after the beta decay of the primary fragments, are and. Calculate Q for this fission process. The relevant atomic and particle masses are

In the fission of, particles decay from the parent nucleus. The nuclear reaction can be written as:

It is given that:

Mass of a nucleus,

Mass of a nucleus,

Mass of a nucleus,

Mass of a neutron,

Q-value of the above equation,

Where,

Represents the corresponding atomic masses of the nuclei

But

Hence, the Q-value of the fission process is.

Q: 28. Consider the D – T reaction (deuterium – tritium fusion)

(A) Calculate the energy released in MeV in this reaction from the data:

(B)Consider the radius of both deuterium and tritium to be approximately. What is the kinetic energy needed to overcome the coulomb repulsion between the two nuclei? To what temperature must the gas be heated to initiate the reaction? (Hint: Kinetic energy required for one fusion event =average thermal kinetic energy available with the interacting particles absolute temperature.)

(A) Take the D-T nuclear reaction:

It is given that:

Mass of

Mass of

Mass of

Mass of

Q-value of the given D-T reaction is:

But

(B) Radius of deuterium and tritium,Distance between the two nuclei at the moment when they touch each other, Charge on the deuterium nucleus

Charge on the tritium nucleus

Hence, the repulsive potential energy between the two nuclei is given as:

Where,

Permittivity of free space

Hence, or of kinetic energy is needed to overcome the Coulomb repulsion between the two nuclei.

However, it is given that:

Where,

Boltzmann constant

Temperature required for triggering the reaction

Hence, the gas must be heated to a temperature of to initiate the reaction.

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