The numbers of nuclei of a radioactive substance at time t = 0 are 1000 and 900 at time t = 2 s. Then number of nuclei at time t = 4 s will be

(1) 800            (2) 810             (3) 790             (4) 700

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A nucleus ${}_{Z}{}^{A}X$ has mass represented by m(A, Z). If ${m}_{p}$ and ${m}_{n}$ denote the mass of proton and neutron respectively and BE the binding energy (in MeV), then 

(1) BE = [m(A, Z) - Z${m}_{p}$- (A - Z)${m}_{n}$${c}^{2}$

(2) BE = [Z${m}_{p}$+ (A - Z)${m}_{n}$- m(A,Z)] ${c}^{2}$

(3) BE = [Z${m}_{p}$+ A${m}_{n}$- m(A, Z)] ${c}^{2}$

(4) BE = m(A, Z) - Z${m}_{p}$- (A, Z)${m}_{n}$

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Nuclear binding energy
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The equation  is          (UP CPMT 2002)

(1) $\beta$-emission                (2) $\alpha$-emission

(3) ${e}^{-}$ capture                (4) fission

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Types of decay
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Half-lives of two radioactive substances A and B respectively 20 min and 40 min.  Initially, the samples of A and B have equal number of nuclei. After 80 min the ratio of remaining number of A and B nuclei is 

(1) 1 : 16                         (2) 4 : 1

(3) 1 : 4                           (4) 1 : 1

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Radioactive ${}_{27}{}^{60}Co$ is transformed into stable ${}_{28}{}^{60}Ni$ by emitting two $\gamma$-rays of energies [Kerala PET 2010]

(1) 1.33 MeV and 1.17 MeV in succession

(2) 1.17 MeV and 1.33 MeV in succession

(3) 1.37 MeV and 1.13 MeV in succession

(4) 1.17 MeV and 1.13 MeV in succession

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The volume occupied by an atom is greater than the volume of the nucleus by factor of about 

(1) ${10}^{10}$                (2) ${10}^{15}$                (3) ${10}^{1}$                (4) ${10}^{5}$

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Mass-energy equivalent
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A radioactive nucleus undergoes a series of decay according to the scheme

$A\stackrel{\alpha }{\to }{A}_{1}\stackrel{\beta }{\to }{A}_{2}\stackrel{\alpha }{\to }{A}_{3}\stackrel{\gamma }{\to }{A}_{4}$

If the mass number and atomic number of A are 180 and 72 respectively, then what are these number for ${A}_{4}$?

(1) 172 and 69                         (2) 174 and 70

(3) 176 and 69                         (4) 176 and 70

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What fraction of a radioactive material will get disintegrated in a period of two half-lives.

(1) whole                (2) half                (3) one-fourth                (4) three-fourth

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If the nucleus ${}_{13}{}^{27}Al$ has a nuclear radius of about 3.6 fm, then ${}_{52}{}^{125}Te$ would have its radius approximately as 

(1) 6.0 fm                   (2) 9.6 fm                 (3) 12.0 fm                   (4) 4.8 fm

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Mass-energy equivalent
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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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