The counting rate observed from a radio active source at t = 0 second was 1600 counts per second and at t = 8 seconds it was 100 counts per second. The counting rate observed, as counts per second, at t = 6 seconds will be

(1) 400         (2) 300         (3) 200        (4) 150

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If ${N}_{0}$ is the original mass of the substance of half life period ${T}_{1/2}$= 5 years, then the amount of substance left after 15 years is [AIEEE 2012]

(1) ${N}_{0}$/8           (2) ${N}_{0}$/16           (3) ${N}_{0}$/2            (4) ${N}_{0}$/4

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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 [2007]

(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 [1998]

(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 [2003]

(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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