After two hours, one-sixteenth of the starting amount of a certain radioactive isotope remained undecayed. The half life of the isotope is [Bihar MEE 1995; Manipal MEE 1995; MP PMT 1997; AFMC 2000, 05; DPMT 2002]

(1) 15 minutes                   (2) 30 minutes

(3) 45 minutes                   (4) 1 hour

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Atomic weight of boron is 10.81 and it has two isotopes . Then, the ratio of atoms of   in nature would be

(1) 19 : 81                   (2) 10 : 11                (3) 15 : 16                 (4) 81 : 19

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Mass-energy equivalent
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The half-life of radium is 1600 yr.  The fraction of a sample of radium that would remain

after 6400 yr 

(1) $\frac{1}{4}$                (2) $\frac{1}{2}$                 (3) $\frac{1}{8}$                   (4) $\frac{1}{16}$

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The count rate of a Geiger Muller counter for the radiation of a radioactive material of half-life 30 min decreases to 5 ${s}^{-1}$ after 2 h. The initial count rate was 

(1) 20 ${s}^{-1}$             (2) 25 ${s}^{-1}$             (3) 80 ${s}^{-1}$              (4) 625 ${s}^{-1}$

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An element A decays into element C by a two step process

$A\to B+{}_{2}H{e}^{4}\phantom{\rule{0ex}{0ex}}B\to C+2{e}^{-}$

then  

(1) A and C are isotopes

(2) A and C are isobars

(3) A and B are isotopes

(4) A and B are isobars

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Types of decay
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The radius R of a nuclear matter varies with A as

(1)                          (2)

(3)                              (4)

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Mass-energy equivalent
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Number of nuclei of a radioactive substance at time t = 0 are 2000 and 1800 at time t = 2s. Number of nuclei left after t = 6s is [MGIMS 2010]

(1) 1442               (2) 1554                 (3) 1652                 (4) 1458

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In a radioactive material the activity at time ${t}_{1}$ is ${R}_{1}$ and at a later time ${t}_{2}$, it is ${R}_{2}$. If the decay constant of the material is $\lambda$, then

(a) ${R}_{1}={R}_{2}{e}^{-\lambda \left({t}_{1}-{t}_{2}\right)}$                                    (b) ${R}_{1}={R}_{2}{e}^{\lambda \left({t}_{1}-{t}_{2}\right)}$

(c) ${R}_{1}={R}_{2}\left(\frac{{t}_{2}}{{t}_{1}}\right)$                                          (d) ${R}_{1}={R}_{2}$

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Which of the following are suitable for the fusion process ? 

(1) Light nuclei

(2) Heavy nuclei

(3) Elements lying in the middle of periodic table

(4) Elements lying in the middle of binding energy curve

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Nuclear binding energy
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An archeologist analyses the wood in a prehistoric structure and finds that ${\mathrm{C}}^{14}$ (Half - life=5700 years) to ${\mathrm{C}}^{12}$ is only one - fourth of that found in the cells buried plants. The age of the wood is about

1. 5700 yr

2. 2850 yr

3. 11,400 yr

4. 22,800 yr

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