Radioactive material A has decay constant 8$\lambda$ and material B has decay constant $\lambda$ Initially, they have same number of nuclei. After what time, the ratio of number of nuclei of material B to that A will be $\frac{1}{e}$?

(a) $\frac{1}{\lambda }$

(b) $\frac{1}{7\lambda }$

(c) $\frac{1}{8\lambda }$

(d)$\frac{1}{9\lambda }$

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The half-life of a radioactive substance is  30 minutes. The time (in minute) taken between 40% decay and 85% decay of the same radioactive substance is

(a) 15           (b) 30

(c) 45           (d) 60

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(a)(53/13)1/3 RAl

(b)5/3 RAl

(c)3/5 RAl

(d)(13/53)1/3RAl

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A nucleus of uranium decays at rest into nuclei of thorium and helium. Then,

(a) the helium nucleus has more kinetic energy than the thorium nucleus

(b) the helium nucleus has less momentum than the thorium nucleus

(c) the helium nucleus has more momentum than the thorium nucleus

(d) the heium nucleus has less kinetic energy than the thonum nucleus

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The binding energy per nucleon of  and nuclei are 5.60meV and 7.06meV, respectively.
In the nuclear reaction   , the value of energy Q released is -

(a)19.6MeV

(b)-2.4MeV

(c)8.4MeV

(d)17.3MeV

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A radioisotope X with a half-life 1.4x109 yr decays of Y which is stable. A sample of the rock from a cave was found to contain X and Y in the ratio 1:7. The age of the rock is

(a)1.96x109 yr

(b)3.92x109 yr

(c)4.20x109 yr

(d)8.40x10yr

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The half-life of a radioactive isotope X is 20 yr. It decays to another element Y which is stable. The two elements X and Y were found to be in the ratio 1:7 in a sample of a given rock. The age of the rock is estimated to be

(a) 40 yr

(b) 60 yr

(c) 80 yr

(d) 100 yr

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A certain mass of hydrogen is changed to helium by the process of fusion. The mass defect in fusion reaction is 0.02866 u. The energy liberated per nucelon is (given 1 u = 931 MeV)

(a) 2.67 MeV

(b) 26.7 MeV

(c) 6.675 MeV

(d) 13.35 MeV

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Mass-energy equivalent
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If the nuclear radius of ${}_{27}Al$ is 3.6 Fermi, the approximate nuclear radius of ${}_{64}Cu$ in Fermi is

(a)2.4                                         (b)1.2

(c)4.8                                         (d)3.6

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Mass-energy equivalent
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A mixture consists of two radioactive materials ${A}_{1}$ and ${A}_{2}$ with half lives of 20 s and 10 s respectively.Initially the mixture has 40g of ${A}_{1}$ and 160g of ${A}_{2}$. The amount of the two in the mixture will become equal after

(a)60 s                                      (b)80 s

(c)20 s                                      (d) 40 s

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