A nucleus of mass number \(189\) splits into two nuclei having mass numbers \(125\) and \(64.\) The ratio of the radius of two daughter nuclei respectively is:
1. \(25:16\) 2. \(1:1\)
3. \(4:5\) 4. \(5:4\)

Subtopic:  Nucleus |
 80%
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NEET - 2022
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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 '\(ln N\)' 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.  \(-\lambda^{-1}\)

Subtopic:  Radioactivity (OLD NCERT) |
 68%
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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.  \(\frac{e-1}{e}\)

Subtopic:  Radioactivity (OLD NCERT) |
From NCERT
NEET - 2022
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Given below are two statements: 
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 \(t=0.\)
 In the light of the above statements, choose the most appropriate answer from the options given below:
 
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.
 



 
Subtopic:  Radioactivity (OLD NCERT) |
 56%
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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.  \(\frac{1}{5\lambda}\)
Subtopic:  Radioactivity (OLD NCERT) |
 73%
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In the given nuclear reaction, the element \(\mathrm{X}\) is:

\({ }_{11}^{22} \mathrm{Na} \rightarrow \mathrm{X}+\mathrm{e}^{+}+\nu\)
1. \({ }_{12}^{22} \mathrm{Mg}\)
2. \({ }_{11}^{23} \mathrm{Na}\)
3. \({ }_{10}^{23} \mathrm{Ne}\)
4. \(_{10}^{22}\textrm{Ne}\)
Subtopic:  Types of Decay |
 64%
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The half-life of a radioactive substance is \(20\) minutes. In how much time, the activity of substance drops to \((\frac{1}{16})^{\mathrm{th}}\) of its initial value?
1. \(80\) minutes
2. \(20\) minutes
3. \(40\) minutes
4. \(60\) minutes
Subtopic:  Radioactivity (OLD NCERT) |
 51%
From NCERT
NEET - 2023
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The half-life of a radioactive nuclide is 100 hours. The fraction of original activity that will remain after 150 hours would be:

1. 23

2. 232

3. 1/2

4. 122

Subtopic:  Radioactivity (OLD NCERT) |
 60%
From NCERT
NEET - 2021
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A radioactive nucleus \(_{\mathrm{Z}}^{\mathrm{A}}\mathrm{X}\) undergoes spontaneous decay in the sequence \(_{\mathrm{Z}}^{\mathrm{A}}\mathrm{X}\rightarrow \mathrm{B}_{\mathrm{Z-1}}\rightarrow \mathrm{C}_{\mathrm{Z-3}}\rightarrow \mathrm{D}_{\mathrm{Z-2}}\) where \(\mathrm{Z}\) is the atomic number of element \(\mathrm{X}\). The possible decay particles in the sequence are: 

1. \(\beta^{+}, ~\alpha, ~\beta^{-}\) 2. \(\beta^{-}, ~\alpha, ~\beta^{+}\)
3. \(\alpha, ~\beta^{-},~\beta^{+}\) 4. \(\alpha, ~\beta^{+},~\beta^{-}\)
Subtopic:  Types of Decay |
 69%
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A nucleus with mass number \(240\) breaks into fragments each of mass number \(120\). The binding energy per nucleon of unfragmented nuclei is \(7.6\) MeV while that of fragments is \(8.5~\text{MeV}\). The total gain in the binding energy in the process is:


1. \(804\) MeV 
2. \(216\) MeV
3. \(0.9\) MeV
4. \(9.4\) MeV
Subtopic:  Nuclear Binding Energy |
 62%
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NEET - 2021
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