The half life of radium is 1620 years and its atomic weight is 226 kgm per kilomol. The number of atoms that will decay from its 1 gm sample per second will be

(a) $3.61×{10}^{10}$     (b) $3.6×{10}^{12}$
(c) $3.11×{10}^{15}$     (d) $31.1×{10}^{15}$

(Avogardo's number N = $6.02×{10}^{26}$ atpm/kilomol)

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A radioactive material decays by simultaneous emission of two particles with respective half lives 1620 and 810 years. The time (in years) after which one- fourth of the material remains is
(a) 1080         (b) 2430
(c) 3240         (d) 4860

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The half life period of a radioactive element X is same as the mean life time of another radioactive element Y. Initially both of them have the same number of atoms. Then

(a) X and Y have the same decay rate initially
(b) X and Y decay at the same rate always
(c) Y will decay at a faster rate than X
(d) X will decay at a faster rate than Y

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For a substance the average life for $\mathrm{\alpha }$-emission is 1620 years and for $\mathrm{\beta }$ emission is 405 years. After how much time the 1/4 of the material remains after $\mathrm{\alpha }$ and $\mathrm{\beta }$ emission

1. 1500 years            2. 300 years
3. 449 years              4. 810 years

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Types of decay
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A radioactive nucleus undergoes $\mathrm{\alpha }$-emission to form a stable element. What will be the recoil velocity of the daughter nucleus if v is the velocity of $\mathrm{\alpha }$-particle and A is the atomic mass of radioactive nucleus ?

1. $\frac{4\mathrm{V}}{\mathrm{A}-4}$             2. $\frac{2\mathrm{V}}{\mathrm{A}-4}$
3. $\frac{4\mathrm{V}}{\mathrm{A}+4}$             4. $\frac{2\mathrm{V}}{\mathrm{A}+4}$

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Types of decay
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Half life of a radio-active substance is 20 minutes. The time between 20% and 80% decay will be
1. 20 minutes          2. 40 minutes
3. 30 minutes          4. 25 minutes

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After 280 days, the activity of a radioactive sample is 6000 dps. The activity reduces to 3000 dps after another 140 days. The initial activity of the sample in dps is

(a) 6000            (b) 9000
(c) 3000            (d) 24000

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Excitation energy of a hydrogen like ion in its first excitation state is 40.8 eV. Energy needed to remove the electron from the ion in ground state is
(a) 54.4 eV             (b) 13.6 eV
(c) 40.8 eV             (d) 27.2 eV

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Mass-energy equivalent
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Consider a hydrogen like atom whose energy in nth exicited state is given by  when this excited atom makes a transition from excited state to ground state, most energetic photons have energy ${\mathrm{E}}_{\mathrm{max}}$ = 52.224 eV and least energetic photons have energy ${\mathrm{E}}_{\mathrm{min}}$ = 1.224 eV. The atomic number of atom is
(a) 2                 (b) 5
(c) 4                 (d) None of these

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Mass-energy equivalent
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A radioactive sample is $\mathrm{\alpha }$-emitter with half life 138.6 days is observed by a student to have 2000 disintegration/sec. The number of radioactive nuclei for given activity are
(a) $3.45×{10}^{10}$               (b) $1×{10}^{10}$
(c) $3.45×{10}^{15}$               (d) $2.75×{10}^{11}$

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