average life of a radioactive sample is 4ms initially the

Average life of a radioactive sample is $$4\,ms.$$ Initially the total number of nuclei is $${N_0}.$$ A charged capacitor of capacity $$20\,\mu F$$ is connected across a resistor $$R.$$ The value of $$R$$ such that ratio of number of nuclei remaining to charge on capacitor remains constant with time is

A. $$100\,\Omega $$

B. $$200\,\Omega $$

C. $$300\,\Omega $$

D. $$400\,\Omega $$

Answer : $$200\,\Omega $$

Solution :
$$\eqalign{ & N = {N_0}{e^{ - \lambda t}}q = {q_0}{e^{\frac{{ - t}}{{RC}}}}\,{\text{and}}\,\,\frac{N}{q} = {\text{constant}} \cr & {\text{when}}\,{e^{ - \lambda t}} = {e^{\frac{t}{{RC}}}} \cr & \Rightarrow \lambda = \frac{1}{{RC}}R = 200\,\Omega . \cr} $$

Releted MCQ Question on
Modern Physics >> Radioactivity

Releted Question 1

An alpha particle of energy $$5\,MeV$$ is scattered through $${180^ \circ }$$ by a fixed uranium nucleus. The distance of closest approach is of the order of

A. $$1\, \mathop {\text{A}}\limits^ \circ $$

B. $${10^{ - 10}}cm$$

C. $${10^{ - 12}}cm$$

D. $${10^{ - 15}}cm$$

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Releted Question 2

Beta rays emitted by a radioactive material are

A. electromagnetic radiations

B. the electrons orbiting around the nucleus

C. charged particles emitted by the nucleus

D. neutral particles

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Releted Question 3

Consider $$\alpha $$ particles, $$\beta $$ particles and $$\gamma $$ - rays, each having an energy of $$0.5\,MeV.$$ In increasing order of penetrating powers, the radiations are:

A. $$\alpha ,\beta ,\gamma $$

B. $$\alpha ,\gamma ,\beta $$

C. $$\beta ,\gamma ,\alpha $$

D. $$\gamma ,\beta ,\alpha $$

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Releted Question 4

A radioactive material decays by simultaneous emission of two particles with respective half-lives 1620 and 810 years. The time, in years, after which one-fourth of the material remains is

A. 1080

B. 2430

C. 3240

D. 4860

View Answer

Releted MCQ Question on
Modern Physics >> Radioactivity

An alpha particle of energy $$5\,MeV$$ is scattered through $${180^ \circ }$$ by a fixed uranium nucleus. The distance of closest approach is of the order of

Beta rays emitted by a radioactive material are

Consider $$\alpha $$ particles, $$\beta $$ particles and $$\gamma $$ - rays, each having an energy of $$0.5\,MeV.$$ In increasing order of penetrating powers, the radiations are:

A radioactive material decays by simultaneous emission of two particles with respective half-lives 1620 and 810 years. The time, in years, after which one-fourth of the material remains is

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Radioactivity

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Releted MCQ Question on Modern Physics >> Radioactivity

An alpha particle of energy $$5\,MeV$$ is scattered through $${180^ \circ }$$ by a fixed uranium nucleus. The distance of closest approach is of the order of

Beta rays emitted by a radioactive material are

Consider $$\alpha $$ particles, $$\beta $$ particles and $$\gamma $$ - rays, each having an energy of $$0.5\,MeV.$$ In increasing order of penetrating powers, the radiations are:

A radioactive material decays by simultaneous emission of two particles with respective half-lives 1620 and 810 years. The time, in years, after which one-fourth of the material remains is

Practice More Releted MCQ Question on Radioactivity

Practice More MCQ Question on Physics Section

Releted MCQ Question on
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