Q. No.At any instant, two elements X1 and X2 have the same number of radioactive atoms. If the decay constant of X1 and X2 are 10 \(\lambda\) and \(\lambda\) respectively, then the time when the ratio of their atoms becomes \(\frac1e\) will be:
1. \(\frac{1}{11\lambda}\)
2. \(\frac{1}{9\lambda}\)
3. \(\frac{1}{6\lambda}\)
4. \(\frac{1}{5\lambda}\)
| Statement-I: | The law of radioactive decay states that the number of nuclei undergoing the decay per unit time is inversely proportional to the total number of nuclei in the sample. |
| Statement-II: | The half life of a radionuclide is the sum of the left time of all nuclei, divided by the initial concentration of the nuclei at time \(t=0.\) |
| 1. | Both Statement-I and Statement-II are correct. |
| 2. | Both Statement-I and Statement-II are incorrect. |
| 3. | Statement-I is correct but Statement-II is incorrect. |
| 4. | Statement-I is incorrect but Statement-II is correct. |
The fraction of the original number of radioactive atoms that disintegrates (decays) during the average lifetime of a radioactive substance will be:
1. \(\frac{1}{e}\)
2. \(\frac{1}{1+e}\)
3. \(\frac{e-1}{e+1}\)
4. \(\frac{e-1}{e}\)
At some instant, the number of radioactive atoms in a sample is \(N_0\) and after time \(t\), the number decreases to \(N\). It is found that the graphical representation \(\mathrm{ln} N\) versus \(t\) along the \(y\) and \(x\) axis respectively is a straight line. Then the slope of this line is:
1. \(\lambda\)
2. \(-\lambda\)
3. \(\lambda^{-1}\)
4. \(-\lambda^{-1}\)
| 1. | \(25:16\) | 2. | \(1:1\) |
| 3. | \(4:5\) | 4. | \(5:4\) |
\({ }_{11}^{22} \mathrm{Na} \rightarrow \mathrm{X}+\mathrm{e}^{+}+\nu\)
| 1. | \({ }_{12}^{22} \mathrm{Mg}\) | 2. | \({ }_{11}^{23} \mathrm{Na}\) |
| 3. | \({ }_{10}^{23} \mathrm{Ne}\) | 4. | \(_{10}^{22}\textrm{Ne}\) |
1. \(80\) minutes
2. \(20\) minutes
3. \(40\) minutes
4. \(60\) minutes
The half-life of a radioactive nuclide is 100 hours. The fraction of original activity that will remain after 150 hours would be:
1.
2.
3.
4.
| 1. | \(\beta^{+}, ~\alpha, ~\beta^{-}\) | 2. | \(\beta^{-}, ~\alpha, ~\beta^{+}\) |
| 3. | \(\alpha, ~\beta^{-},~\beta^{+}\) | 4. | \(\alpha, ~\beta^{+},~\beta^{-}\) |
A nucleus with mass number \(240\) breaks into fragments each of mass number \(120.\) The binding energy per nucleon of unfragmented nuclei is \(7.6~\text{MeV}\) while that of fragments is \(8.5~\text{MeV}.\) The total gain in the binding energy in the process is:
1. \(804~\text{MeV}\)
2. \(216~\text{MeV}\)
3. \(0.9~\text{MeV}\)
4. \(9.4~\text{MeV}\)
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