# 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

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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

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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

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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. ${R}_{1}={R}_{2}$

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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

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Two radioactive substances A and B have decay constant 5λ and λ 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 (1/e)2 after a time interval of:

1. $\frac{1}{4\mathrm{\lambda }}$  

2. $4\mathrm{\lambda }$  

3. $2\mathrm{\lambda }$ 

4.  $\frac{1}{2\mathrm{\lambda }}$

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AIIMS - 2007
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The activity of the radioactive element decreases to one-third of the original activity ${\mathrm{A}}_{0}$ in a period of 7 years. After a further lapse of 7 years, its activity will be:

1.  ${\mathrm{A}}_{0}$  

2.  $\frac{2}{3}{\mathrm{A}}_{0}$  

3.  $\frac{{\mathrm{A}}_{0}}{6}$  

4.  $\frac{{\mathrm{A}}_{0}}{9}$

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A radioactive nucleus X decays to a stable nucleus 'y'. The graph of the rate of formation of 'y' against time 't' will be:

 1 2 3 4
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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.

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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