Which is the correct expression for half-life

(a) ${\mathrm{t}}_{1/2}=\mathrm{log}2$                  (b) ${\mathrm{t}}_{1/2}=\frac{\mathrm{\lambda }}{\mathrm{log}2}$
(c) ${\mathrm{t}}_{1/2}=\frac{\mathrm{\lambda }}{\mathrm{log}2}\left(2.303\right)$      (d)

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A nucleus ${}_{\mathrm{Z}}{}^{\mathrm{A}}\mathrm{A}$ emits an $\mathrm{\alpha }$-particle. The resultant nucleus emits a ${\mathrm{\beta }}^{+}$ particle. The respective atomic and mass no. of the final nucleus will be
(a) Z – 3, A – 4            (b) Z – 1, A – 4
(c) Z – 2, A – 4            (d) Z, A – 2

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Types of decay
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The activity of a radioactive sample is 1.6 curie and its half-life is 2.5 days. Its activity after 10 days will be

(a) 0.8 curie       (b) 0.4 curie
(c) 0.1 curie       (d) 0.16 curie

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In a mean life of a radioactive sample
(a) About 1/3 of substance disintegrates
(b) About 2/3 of the substance disintegrates
(c) About 90% of the substance disintegrates
(d) Almost all the substance disintegrates

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Three fourth of the active decays in a radioactive sample in 3/4 sec. The half life of the sample is
(a) $\frac{1}{2}$ sec            (b) 1 sec
(c) $\frac{3}{8}$ sec            (d) $\frac{3}{4}$ sec

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During mean life of a radioactive element, the fraction that disintegrates is
(a) e            (b)  $\frac{1}{\mathrm{e}}$
(c) $\frac{\mathrm{e}-1}{\mathrm{e}}$     (d) $\frac{\mathrm{e}}{\mathrm{e}-1}$

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1 Curie is equal to
(a) $3×{10}^{10}$ disintegrations/sec
(b) $3.7×{10}^{7}$ disintegrations/sec
(c) $5×{10}^{7}$ disintegrations/sec
(d) $3.7×{10}^{10}$ disintegrations/sec

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The electron emitted in beta radiation originates from

(a) Inner orbits of atoms
(b) Free electrons existing in nuclei
(c) Decay of a neutron in a nucleus
(d) Photon escaping from the nucleus

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Types of decay
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When a radioactive substance emits an $\mathrm{\alpha }$-particle, its position in the periodic table is lowered by

(a) One place               (b) Two places
(c) Three places           (d) Four places

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Types of decay
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During negative $\mathrm{\beta }$-decay
(a) Neutron converts into proton
(b) Proton converts into neutron
(c) Neutron proton ratio increases
(d) None of these

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Types of decay