If a radioactive nucleus decays according to the following reaction

${}_{72}X_{180}\stackrel{\alpha }{\to }{X}_{1}\stackrel{\beta }{\to }{X}_{2}\stackrel{\alpha }{\to }{X}_{3}\stackrel{\gamma }{\to }{X}_{4}$

then the mass number and the atomic number of ${X}_{4}$ then the mass number and the atomic number of ${X}_{4}$ will be, respectively [MP PET 2002]

(1) 172, 70                     (2) 172, 69

(3) 172, 68                     (4) 171, 69

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Difficulty Level:

Two radioactive materials ${X}_{1}$ and ${X}_{2}$ have decay constants 10$\lambda$ and $\lambda$ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of ${X}_{1}$ to that of ${X}_{2}$ will be $\frac{1}{e}$ after a time

(1)                      (2)

(3)                      (4)

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Difficulty Level:

A radioactive material has mean-lives of 1620 yr and 520 yr for $\alpha$ and $\beta$-emission. The material decays by simultaneous $\alpha$ and $\beta$-emission. The time in which 1/4th of the material remains intact is

(a) 4675 yr                                 (b) 720 yr

(c) 545 yr                                   (d) 324 yr

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Difficulty Level:

The radioactivity of an element becomes $\frac{1}{64}th$ of its original value in 60 seconds. Then the half value period is

(1) 5 sec              (2) 10 sec            (3) 20 sec            (4) 30 sec

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Difficulty Level:

A nucleus of ${}_{84}{}^{210}Po$ originally at rest emits $\alpha$ particle with speed $\nu$. What will be the recoil speed of the daughter necleus. [DCE 2002]

(1) 4$\nu$ / 206                          (2) 4$\nu$ / 214

(3) $\nu$ / 206                            (4) $\nu$ / 214

Concept Questions :-

Types of decay
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Difficulty Level:

An atom of mass number 15 and atomic number 7 captures an $\alpha$-particle and then emits a proton. The mass number and atomic number of the resulting product will respectively be

(1) 14 and 2                          (2) 15 and 3

(3) 16 and 4                          (4) 18 and 8

Concept Questions :-

Types of decay
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Difficulty Level:

If radius of the ${}_{13}{}^{27}\mathrm{Al}$ nucleus is estimated to be 3.6 fermi then the radius of ${}_{52}{}^{125}Te$ nucleus be nearly

(a) 4 Fermi                                     (b) 5 Fermi

(c) 6 Fermi                                     (d) 8 Fermi

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Mass-energy equivalent
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Difficulty Level:

Solar energy is mainly caused due to 

(1) fusion of protons during synthesis of heavier elements

(2) gravitational contraction

(3) burning of hydrogen in the oxygen

(4) fission of uranium present in the sun

Concept Questions :-

Mass-energy equivalent
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Difficulty Level:

A sample of radioactive elements contains $4×{10}^{10}$ active nuclei. If half-life of element is 10 days, then the number of decayed nuclei after 30 days is 

(1) $0.5×{10}^{10}$                   (2) $2×{10}^{10}$

(3) $3.5×{10}^{10}$                   (4) $1×{10}^{10}$

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Difficulty Level:

A and B are two radioactive substances whose half-lives are 1 and 2 years respectively. Initially 10 g of A and 1 g of B is taken. The time (approximate) after which they will have the same quantity remaining is

(1) 6.62 yr                (2) 5 yr                (3) 3.2 yr                   (4) 7 yr

Concept Questions :-