Nuclei

Question

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Half-lives of two radioactive substances A and B are respectively 20 min and 40 min. Initially the samples of A and B have equal number of nuclei. After 80 min the ratio of remaining number of A and B nuclei is

1 : 16

4 : 1

1 : 4

1 : 1

Solution

1 : 4

Total number of nuclei remained after n half- lives is

N = N_o ${(\frac{1}{2})}^{n}$

Total time given = 80 min

Number of half-lives of A, n_A = $\frac{80 \min}{20 \min}$

= 4

Number of half-lives of B, n_B = $\frac{80 \min}{40 \min}$

= 2

Number of nuclei remains undecayed

$N = N_{o} {(\frac{1}{2})}^{n}$

Where N_o is initial number of nuclei.

$∴ \frac{N_{A}}{N_{B}} = \frac{{(\frac{1}{2})}^{n_{A}}}{{(\frac{1}{2})}^{n_{B}}}$

$\Rightarrow \frac{N_{A}}{N_{B}} = \frac{{(\frac{1}{2})}^{4}}{{(\frac{1}{2})}^{2}} = \frac{\frac{1}{16}}{\frac{1}{4}}$

$\Rightarrow \frac{N_{A}}{N_{B}} = \frac{1}{4}$

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Nuclei

Half-lives of two radioactive substances A and B are respectively 20 min and 40 min. Initially the samples of A and B have equal number of nuclei. After 80 min the ratio of remaining number of A and B nuclei is

1 : 16

4 : 1

1 : 4

1 : 1

Some More Questions From Nuclei Chapter

If M₀ is the mass of an oxygen isotope ₈O¹⁷ , Mp and M_N are the masses of a proton and a neutron respectively, the nuclear binding energy of the isotope is

In gamma-ray emission from a nucleus

When ₃Li⁷ nuclei are bombarded by protons, and the resultant nuclei are ₄Be⁸ , the emitted particles will be

The ‘rad’ is the correct unit used to report the measurement of

A photocell is illuminated by a small bright source placed 1 m away. When the same source of light is placed 1 /2 m away, the number of electrons emitted by photocathode would

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For Daily Free Study Material Join wiredfaculty

Nuclei

Half-lives of two radioactive substances A and B are respectively 20 min and 40 min. Initially the samples of A and B have equal number of nuclei. After 80 min the ratio of remaining number of A and B nuclei is 1 : 16 4 : 1 1 : 4 1 : 1

Some More Questions From Nuclei Chapter

If M0 is the mass of an oxygen isotope 8O17 , Mp and MN are the masses of a proton and a neutron respectively, the nuclear binding energy of the isotope is

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A photocell is illuminated by a small bright source placed 1 m away. When the same source of light is placed 1 /2 m away, the number of electrons emitted by photocathode would

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Half-lives of two radioactive substances A and B are respectively 20 min and 40 min. Initially the samples of A and B have equal number of nuclei. After 80 min the ratio of remaining number of A and B nuclei is

1 : 16

4 : 1

1 : 4

1 : 1

If M₀ is the mass of an oxygen isotope ₈O¹⁷ , Mp and M_N are the masses of a proton and a neutron respectively, the nuclear binding energy of the isotope is

When ₃Li⁷ nuclei are bombarded by protons, and the resultant nuclei are ₄Be⁸ , the emitted particles will be