Types of Decay

In a radioactive material, the activity at time t₁ is R₁ and at a later time t₂, it is R₂. If the decay constant of the material is \lambda , then:

1. $R_1=R_2{e}^{\mathrm{\backslash lambda}(t_1\mathit{+}{t}_2)}$

2. $R_1=R_2{e}^{-\mathrm{\backslash lambda}(t_1-t_2)}$

3. $R_1=R_2(t_1-t_2)$

4. $R_1=R_2$

In the radioactive decay process, the negatively charged emitted \beta -particles are:

Two radioactive substances A and B have decay constants 5\lambda and \lambda respectively. At t = 0, they have the same number of nuclei. The ratio of the number of nuclei of A to those of B will be $\frac{1}{e^2}$ after a time interval:

1. $\frac{1}{4\mathrm{\backslash lambda}}$

2. $4\mathrm{\backslash lambda}$

3. $2\mathrm{\backslash lambda}$

4. $\frac{1}{2\mathrm{\backslash lambda}}$

The decay constants of two radioactive materials X₁ and X₂ are and respectively. Initially, they have the same number of nuclei. The ratio of the number of nuclei of X₁ to that of X₂ will be after a time:
1.

2.

3.

4.

The number of beta particles emitted by a radioactive substance is twice the number of alpha particles emitted by it. The resulting daughter is an:

The activity of a radioactive sample is measured as N₀ counts per minute at t = 0 and N₀/e counts per minute at t = 5 min. The time (in minutes) at which the activity reduces to half its value is:

1. ${\log }_e\left(\frac{2}{5}\right)$

2. $\frac{5}{{\log }_e\left(2\right)}$

3. 5 ${\log }_{10}2$

4. $5$ ${\log }_{e}2$

The half-life of a radioactive element X is 50 yrs. It decays to another element Y which is stable. The two elements X and Y were found to be in the ratio of 1:15 in a sample of a given rock. The age of the rock was estimated to be:

1. 200 yr

2. 250 yr

3. 100 yr

4. 150 yr

A nucleus emits one $\mathrm{}$ and two The resulting nucleus is:

A mixture consists of two radioactive materials A₁ and A₂ with half-lives of 20 s and 10 s respectively. Initially, the mixture has 40 g of A₁ and 160 g of A₂. The amount of the two in the mixture will become equal after:

1. 60 s

2. 80 s

3. 20 s

4. 40 s

A nucleus of uranium decays at rest into nuclei of thorium and helium. Then:

The half-life of a radioactive substance is 30 minutes. The time (in minutes) taken between 40% decay and 85% decay of the same radioactive substance is:

1. 15

2. 30

3. 45

4. 60

Radioactive material 'A' has decay constant '8 ' and material 'B' has a decay constant ' '. Initially, they have the same number of nuclei. After what time, the ratio of the number of nuclei of material 'A' to that of 'B' will be ?

For radioactive material, the half-life is minutes. If initially, there are number of nuclei, the time taken (in minutes) for the disintegration of nuclei is :
1.
2.
3.
4.

What happens to the mass number and the atomic number of an element when it emits radiation?

The half-life of a radioactive sample undergoing is $1.4\backslash times{10}^{17}$ $\sec$. If the number of nuclei in the sample is $2.0$ $\backslash times$ ${10}^{21}$, the activity of the sample is nearly equal to:

1. ${10}^4$ $Bq$

2. ${10}^5$ $Bq$

3. ${10}^6$ $Bq$

4. ${10}^3$ $Bq$

The half-life of a radioactive nuclide is 100 hours. The fraction of original activity that will remain after 150 hours would be:

1. $\frac{2}{3}$

2. $\frac{2}{3\sqrt{2}}$

3. $1/2$

4. $\frac{1}{2\sqrt{2}}$

Tritium, a radioactive isotope of hydrogen, emits which of the following particles?

1. Gamma $\left(\mathrm{\backslash gamma}\right)$

2. Neutron (n)

3. Beta $\left({\mathrm{\backslash beta}}^{-}\right)$

4. Alpha $\left(\mathrm{\backslash alpha}\right)$