Half life of ${\mathrm{Bi}}^{210}$ is 5 days. If we start with 50,000
atoms of this isotope, the number of atoms left over after 10
days is
(a) 5,000                (b) 25,000
(c) 12,500              (d) 20,000

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A nucleus of atomic mass A and atomic number Z emits $\mathrm{\beta }$-particles. The atomic mass and atomic number of the resulting nucleus are
(a) A, Z              (b) A + 1, Z
(c) A, Z + 1        (d) A-4, Z-2

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Types of decay
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The radioactivity of a certain radioactive element drops to 1/64 of its initial value in 30 seconds. Its half life is

(a) 2 seconds               (b) 4 seconds
(c) 5 seconds               (d) 6 seconds

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(a) Becquerel            (b) Pierre Curie
(c) Roentgen             (d) Rutherford

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The average life T and the decay constant $\mathrm{\lambda }$ of a radioactive nucleus are related as
(a) $\mathrm{T\lambda }=1$               (b) $\mathrm{T}=\frac{0.693}{\mathrm{\lambda }}$
(c) $\frac{\mathrm{T}}{\mathrm{\lambda }}=1$               (d) $\mathrm{T}=\frac{\mathrm{c}}{\mathrm{\lambda }}$

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If T is the half life of a radioactive material, then the fraction that would remain after a time $\frac{\mathrm{T}}{2}$ is
(a) $\frac{1}{2}$              (b) $\frac{3}{4}$
(c) $\frac{1}{\sqrt{2}}$           (d) $\frac{\sqrt{2}-1}{\sqrt{2}}$

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If the decay or disintegration constant of a radioactive substance is $\mathrm{\lambda }$, then its half life and mean life are respectively
(a) $\frac{1}{\mathrm{\lambda }}$ and  $\frac{{\mathrm{log}}_{\mathrm{e}}2}{\mathrm{\lambda }}$              (b) $\frac{{\mathrm{log}}_{\mathrm{e}}2}{\mathrm{\lambda }}$ and $\frac{1}{\mathrm{\lambda }}$

(c) ${\mathrm{\lambda log}}_{\mathrm{e}}2$ and $\frac{1}{\mathrm{\lambda }}$               (d) $\frac{\mathrm{\lambda }}{{\mathrm{log}}_{\mathrm{e}}2}$ and $\frac{1}{\mathrm{\lambda }}$

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Which of the following is in the increasing order for penetrating power
(a) $\mathrm{\alpha },\mathrm{\beta },\mathrm{\gamma }$                (b) $\mathrm{\beta },\mathrm{\alpha },\mathrm{\gamma }$
(c) $\mathrm{\gamma },\mathrm{\alpha },\mathrm{\beta }$                (d) $\mathrm{\gamma },\mathrm{\beta },\mathrm{\alpha }$

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The half life of a radioactive element which has only $\frac{1}{32}$ of its original mass left after a lapse of 60 days is

(a) 12 days                  (b) 32 days
(c) 60 days                  (d) 64 days

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The half-life of ${\mathrm{Bi}}^{210}$ is 5 days. What time is taken by (7/8)th part of the sample to decay
(a) 3.4 days               (b) 10 days
(c) 15 days                (d) 20 days

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