In the nuclear fusion reaction ${}_{1}{}^{2}\mathrm{H}+{}_{1}{}^{3}\mathrm{H}\to {}_{2}{}^{4}\mathrm{He}+\mathrm{n}$ given that the repulsive potential energy between the two nuclei is , the temperature at which the gases must be heated to initiate the reaction is nearly
[Boltzmann’s constant )
(a)            (b)
(c)            (d)

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Mass-energy equivalent
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Difficulty Level:

A nucleus with mass number 220 initially at rest emits an $\mathrm{\alpha }$-particle. If the Q value of the reaction is 5.5 MeV, calculate the kinetic energy of the $\mathrm{\alpha }$-particle

(a) 4.4 MeV             (b) 5.4 MeV
(c) 5.6 MeV             (d) 6.5 MeV

Concept Questions :-

Types of decay
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Difficulty Level:

The half life of radioactive Radon is 3.8 days. The time at the end of which 1/20 th of the Radon sample will remain undecayed is
(Given ${\mathrm{log}}_{10}\mathrm{e}=0.4343$
(a) 3.8 days               (b) 16.5 days
(c) 33 days                (d) 76 days

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Difficulty Level:

If 10% of a radioactive material decays in 5 days, then the amount of original material left after 20 days is approximately
(a) 60%              (b) 65%
(c) 70%              (d) 75%

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Difficulty Level:

A radioactive isotope X with a half-life of $1.37×{10}^{9}$ years decays to Y which is stable. A sample of rock from the moon was found to contain both the elements X and Y which were in the ratio of 1 : 7. The age of the rock is
(a) $1.96×{10}^{8}$ years         (b) $3.85×{10}^{9}$ years
(c) $4.11×{10}^{9}$years          (d) $9.59×{10}^{9}$ years

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Difficulty Level:

From a newly formed radioactive substance (Half life 2 hours), the intensity of radiation is 64 times the permissible safe level. The minimum time after which work can be done safely from this source is

(a) 6 hours            (b) 12 hours
(c) 24 hours          (d) 128 hours

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Difficulty Level:

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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Difficulty Level:

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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Difficulty Level:

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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Difficulty Level:

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

Concept Questions :-

Types of decay