a radioactive substance with decay constant of 05s pow 1 is

A radioactive substance with decay constant of $$0.5\,{s^{ - 1}}$$ is being produced at a constant rate of $$50$$ nuclei per second. If there are no nuclei present initially, the time (in second) after which $$25$$ nuclei will be present is

A. $$1$$

B. $$\ln 2$$

C. $$\ln \left( {\frac{4}{3}} \right)$$

D. $$2\ln \left( {\frac{4}{3}} \right)$$

Answer : $$2\ln \left( {\frac{4}{3}} \right)$$

Solution :
$$\eqalign{ & \frac{{dN}}{{dt}} = 50 - \frac{N}{{0.5}} \cr & \int\limits_0^N {\frac{{dN}}{{50 - 2N}}} = \int\limits_0^t {dt} \cr & N = \left( {100\left( {1 - {e^{\frac{{ - t}}{2}}}} \right)} \right) = 25 \cr & t = 2\ln \left( {\frac{4}{3}} \right) \cr} $$

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

View Answer

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

A radioactive substance with decay constant of $$0.5\,{s^{ - 1}}$$ is being produced at a constant rate of $$50$$ nuclei per second. If there are no nuclei present initially, the time (in second) after which $$25$$ nuclei will be present is

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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A radioactive substance with decay constant of $$0.5\,{s^{ - 1}}$$ is being produced at a constant rate of $$50$$ nuclei per second. If there are no nuclei present initially, the time (in second) after which $$25$$ nuclei will be present is

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

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Releted MCQ Question on
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