In a radioactive substance at t = 0, the number of atoms is 8$×{10}^{4}$, its half-life period is 3 yr. The number of atoms equal to $1×{10}^{4}$ will remain after an interval of:

1. 9 yr

2. 8 yr

3. 6 yr

4. 24 yr

Subtopic:  Radioactivity (OLD NCERT) |
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In a radioactive sample the fraction of initial number of radioactive nuclei, which remains undecayed after n mean lives is:

1. $\frac{1}{{e}^{n}}$

2.  ${e}^{n}$

3. $1-\frac{1}{{e}^{n}}$

4. ${\left(\frac{1}{e-1}\right)}^{n}$

Subtopic:  Radioactivity (OLD NCERT) |
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At time t = 0, N1 nuclei of decay constant λ1 and N2 nuclei of decay constant λ2 are mixed. The decay rate of the mixture is:

1. $-{N}_{1}{N}_{2}{e}^{-\left({\lambda }_{1}+{\lambda }_{2}\right)t}$ 

2. $-\left(\frac{{N}_{1}}{{N}_{2}}\right)$ ${e}^{{}^{-\left({\lambda }_{1}+{\lambda }_{2}\right)t}}$ 

3. $-\left({N}_{1}{\lambda }_{1}{e}^{-{\lambda }_{1}t}\right)$ $+$ ${N}_{2}{\lambda }_{2}{e}^{-{\lambda }_{2}t}$ 

4. $-{N}_{1}{\lambda }_{1}{N}_{2}{\lambda }_{2}{e}^{{}^{-\left({\lambda }_{1}+{\lambda }_{2}\right)t}}$

Subtopic:  Radioactivity (OLD NCERT) |
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The half-life period of a radioactive substance is 6 h.  If after 24 h, activity is 0.01 $\mu$Ci, what was the initial activity?

1. 0.04 $\mu$Ci

2. 0.08 $\mu$Ci

3. 0.24 $\mu$Ci

4. 0.16 $\mu$Ci

Subtopic:  Radioactivity (OLD NCERT) |
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The rate of disintegration of a fixed quantity of a radioactive substance can be increased by:

1. increasing the temperature.

2. increasing the pressure.

3. chemical reaction.

4. it is not possible.

Subtopic:  Radioactivity (OLD NCERT) |
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The counting rate observed from a radioactive source at t = 0 second was 1600 counts per second and at t = 8 seconds it was 100 counts per second. The counting rate observed, as counts per second, at t = 6 seconds will be:

1. 400

2. 300

3. 200

4. 150

Subtopic:  Radioactivity (OLD NCERT) |
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Half-lives of two radioactive substances A and B respectively are 20 min and 40 min.  Initially, the samples of A and B have an equal number of nuclei. After 80 min the ratio of the remaining number of A and B nuclei is:

1. 1 : 16

2. 4 : 1

3. 1 : 4

4. 1 : 1

Subtopic:  Radioactivity (OLD NCERT) |
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What fraction of a radioactive material will get disintegrated in a period of two half-lives?

1. whole

2. half

3. one-fourth

4. three-fourth

Subtopic:  Radioactivity (OLD NCERT) |
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In a radioactive material, the activity at time ${t}_{1}$ is ${R}_{1}$ and at a later time, ${t}_{2}$ is ${R}_{2}$. If the decay constant of the material is $\lambda$, then:

1. ${R}_{1}={R}_{2}{e}^{-\lambda \left({t}_{1}-{t}_{2}\right)}$

2. ${R}_{1}={R}_{2}{e}^{\lambda \left({t}_{1}-{t}_{2}\right)}$

3. ${R}_{1}={R}_{2}\left(\frac{{t}_{2}}{{t}_{1}}\right)$

4. ${R}_{1}={R}_{2}$

Subtopic:  Radioactivity (OLD NCERT) |
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A and B are two radioactive substances whose half-lives are 1 and 2 years respectively. Initially 10 g of A and 1 g of B is taken. The time (approximate) after which they will have the same quantity remaining is:

1. 6.62 yr

2. 5 yr

3. 3.2 yr

4. 7 yr

Subtopic:  Radioactivity (OLD NCERT) |
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