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 ? [2002]

(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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In the nuclear reaction:  the term X will be :

(1) ${}_{5}B_{10}$                  (2) ${}_{5}B_{9}$

(3) ${}_{5}B_{11}$                  (4) ${}_{2}H{e}^{4}$

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Mass-energy equivalent
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10 g of radioactive material of half-life 15 year is kept in store for 20 years. The disintegrated material mass is [Pb. PMT 2002]

(1) 12.5 g               (2) 10.5 g               (3) 6.03 g              (4) 4.03 g

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If a radioactive nucleus decays according to the following reaction

${}_{72}X_{180}\stackrel{\alpha }{\to }{X}_{1}\stackrel{\beta }{\to }{X}_{2}\stackrel{\alpha }{\to }{X}_{3}\stackrel{\gamma }{\to }{X}_{4}$

then the mass number and the atomic number of ${X}_{4}$ then the mass number and the atomic number of ${X}_{4}$ will be, respectively [MP PET 2002]

(1) 172, 70                     (2) 172, 69

(3) 172, 68                     (4) 171, 69

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Two radioactive materials ${X}_{1}$ and ${X}_{2}$ have decay constants 10$\lambda$ and $\lambda$ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of ${X}_{1}$ to that of ${X}_{2}$ will be $\frac{1}{e}$ after a time

(1)                      (2)

(3)                      (4)

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A radioactive material has mean-lives of 1620 yr and 520 yr for $\alpha$ and $\beta$-emission. The material decays by simultaneous $\alpha$ and $\beta$-emission. The time in which 1/4th of the material remains intact is

(a) 4675 yr                                 (b) 720 yr

(c) 545 yr                                   (d) 324 yr

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