Radioactivity & Decay Law

1 Mark Questions

1. Why is it found experimentally difficult to detect neutrinos in nuclear <math>\beta</math>-decay? [All India 2014]

Ans. Neutrinos are difficult to detect because they are massless, have no charge and do not interact with nucleons.

2.Define the activity of a given radioactive substance. Write its SI unit. [All India 2013]

Ans. The activity of a sample is defined as the rate of disintegration taking place in the sample of radioactive substance.

SI unit of activity is Becquerel (Bq).

1 Bq =1 disintegration/second

3. Write any two characteristic properties of nuclear force. [All India 2011]

Ans.Two characteristics of nuclear force are given as below:

1. These are short range forces.
2. These are strong force of attractive nature
3. How is the mean life of a radioactive sample related to its half-life? [Foreign 2011] Ans.

Mean life, <math>t_m = \frac{1}{\lambda}</math>, where <math>\lambda</math> is decay constant.

But half-life, <math>T_{1/2} = \frac{\ln 2}{\lambda}</math>

<math>\Rightarrow</math>

<math display="block">\lambda = \frac{\ln 2}{T_{1/2}}</math>

<math>t_m = \frac{T_{1/2}}{\ln 2} = \frac{T_{1/2}}{0.693}</math>

<math>\Rightarrow</math>

<math>t_m = 1.443 T_{1/2}</math>

1. How is the radius of a nucleus related to its mass number? [All India 2011 c] Ans.

Radius of nucleus, <math>R = R_0 A^{1/3}</math>

where, <math>R = \text{radius of nucleus}</math>

<math>A = mass number</math>

<math>R_0 = 1.2 \text{ fm} = 1.2 \times 10^{-15} \text{m}</math>

6. A nucleus undergoes <math>\beta</math>-decay . How does its

1. mass number
2. atomic number change?

Ans.

During <math>\beta</math>-decay,

1. no change in mass number.
2. atomic number increases by 1.

1. A nucleus <math>^{238}_{92}</math> U undergoes <math>\alpha</math>-decay and transforms to thorium. What is
2. the mass number and
3. atomic number of the nucleus produced? [Delhi 2011C]

Ans.

In <math>\alpha</math>-decay, the mass number of parent nucleus decreases by 4 units and atomic number decreases by 2 units.

<math>^{238}U_{92} \xrightarrow{\alpha-\text{decay}} ^{234}\text{Th}_{90}</math> ٠.

1. Mass number of the nucleus produced <math>= 234</math>

(1/2)

1. Atomic number of nucleus produced =90

(1/2)

1. Two nuclei have mass numbers in the ratio 1: 8. What is the ratio of their nuclear radii? [All India 2009]

Ans.

Radius of nucleus, <math>R = R_0 A^{1/3}</math>

where, <math>R_0</math> = constant, A = mass number

<math display="block">\therefore \frac{R_1}{R_2} = \left(\frac{A_1}{A_2}\right)^{1/3} = \left(\frac{1}{8}\right)^{1/3} = \frac{1}{2}</math>

<math>R_1: R_2 = 1:2</math>

1. Two nuclei have mass numbers in the ratio 8:125. What is the ratio of their nuclear radii?

[All India 2009]

Ans. Refer to ans. 8. (Ans. 2:5)

10.Two nuclei have mass numbers in the ratio 27:125. What is the ratio of their nuclear radii? [All India 2009]

Ans. Refer to ans. 8. (Ans. 3:5)

11.Two nuclei have mass numbers in the ratio 1:2. What is the ratio of their nuclear densities? [Delhi 2009]

Ans. Nuclear density is independent of mass number.

1. Assuming the nuclei to be spherical in shape, how does the surface area of a nucleus of

mass number A1 compare with that of a nucleus of mass number A2? [All India 2008 C] Ans.