# Physics Class 12 NCERT Solutions: Chapter 13 Nuclei Part 5

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Q: 11. Obtain approximately the ratio of the nuclear radii of the gold isotope and the silver isotope

Nuclear radius of the gold isotope

Nuclear radius of the silver isotope

Mass number of gold,

Mass number of silver,

The ratio of the radii of the two nuclei is related with their mass numbers as:

Hence, the ratio of the nuclear radii of the gold and silver isotopes is about.

Q: 12. Find the and the kinetic energy of the emitted α-particle in the of (A) and (B) .

Given,

.

(A) Alpha particle decay of emits a helium nucleus. As a result, its mass number reduces to and its atomic number reduces to. This is shown in the following nuclear reaction.

Value of

Where,

It is given that:

But

Kinetic energy of the α-particle

(B) Alpha particle decay of is shown by the following nuclear reaction.

It is given that:

Mass of

Mass of u

Kinetic energy of the α-particle

Q: 13. The radionuclide decays according to following equation:

The maximum energy of the emitted positron is.

Given the mass values: and , calculate Q and compare it with the maximum energy of the positron emitted

The given nuclear reaction is:

Half-life nuclei,

Atomic mass of

Atomic mass of

Maximum energy possessed by the emitted positron

The change in the Q-value of the nuclear masses of the nucleus is given as:

Where,

Mass of an electron or positron

Speed of light

Respective nuclear masses

If atomic masses are used instead of nuclear masses, then we have to add in the case of and in the case of .

Hence, equation (1) reduces to

Here, and are the atomic masses.

But

The value of Q is almost comparable to the maximum energy of the emitted positron.