${\mathrm{C}}^{14}$ has half life 5700 years. At the end of 11400 years, the actual amount left is

(a) 0.5 of original amount
(b) 0.25 of original amount
(c) 0.125 of original amount
(d) 0.0625 of original amount

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Mean life of a radioactive sample is 100 seconds. Then its half life (in minutes) is
(a) 0.693                (b) 1
(c) ${10}^{-4}$                 (d) 1.155

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${}_{86}{}^{222}\mathrm{A}\to {}_{84}{}^{210}\mathrm{B}$. In this reaction how many $\mathrm{\alpha }$ and $\mathrm{\beta }$ particles are emitted
(a) 6$\mathrm{\alpha }$, 3$\mathrm{\beta }$          (b) 3$\mathrm{\alpha }$, 4$\mathrm{\beta }$
(c) 4$\mathrm{\alpha }$, 3$\mathrm{\beta }$          (d) 3$\mathrm{\alpha }$, 6$\mathrm{\beta }$

Concept Questions :-

Types of decay
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The phenomenon of radioactivity is
(a) Exothermic change which increases or decreases with temperature
(b) Increases on applied pressure
(c) Nuclear process does not depend on external factors
(d) None of the above

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If half life of radium is 77 days. Its decay constant in day will be
(a) $3×{10}^{-13}$/day            (b) $9×{10}^{-3}$/day
(c) $1×{10}^{-3}$/day              (d) $6×{10}^{-3}$/day

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In a sample of radioactive material, what fraction of the initial number of active nuclei will remain undisintegrated after half of a half-life of the sample
(a) $\frac{1}{4}$        (b) $\frac{1}{2\sqrt{2}}$
(c) $\frac{1}{\sqrt{2}}$     (d) $2\sqrt{2}$

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Consider two nuclei of the same radioactive nuclide. One of the nuclei was created in a supernova explosion 5 billion years ago. The other was created in a nuclear reactor 5 minutes ago. The probability of decay during the next time is
(a) Different for each nuclei
(b) Nuclei created in explosion decays first
(c) Nuclei created in the reactor decays first
(d) Independent of the time of creation

Concept Questions :-

Nuclear reactor
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An $\mathrm{\alpha }$-particle of 5 MeV energy strikes with a nucleus of uranium at stationary at an scattering angle of 180o. The nearest distance upto which $\mathrm{\alpha }$-particle reaches the nucleus will be of the order of
(a) 1 Å               (b)
(c)       (d)

Concept Questions :-

Types of decay
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In a hypothetical Bohr hydrogen, the mass of the electron is doubled. The energy ${\mathrm{E}}_{0}$ and the radius ${\mathrm{r}}_{0}$ of the first orbit will be (${\mathrm{a}}_{0}$ is the Bohr radius)
(a)
(b)
(c)
(d)

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A double charged lithium atom is equivalent to hydrogen whose atomic number is 3. The wavelength of required radiation for exciting electron from first to third Bohr orbit in ${\mathrm{Li}}^{++}$ will be (Ionisation energy of hydrogen atom is 13.6eV)
(a) 182.51 Å                 (b) 177.17 Å
(c) 142.25 Å                 (d) 113.74 Å

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