The half-life of a radioactive substance is  30 minutes. The time (in minute) taken between 40% decay and 85% decay of the same radioactive substance is

1. 15           

2. 30

3. 45           

4. 60

If the radius of the ₁₃Al²⁷ nucleus is taken to R_Al then the radius of ₅₃Te¹²⁵ nucleus is nearly

1. (53/13)^1/3 R_Al

2. 5/3 R_Al

3. 3/5 R_Al

4. (13/53)^1/3 R_Al

A nucleus of uranium decays at rest into nuclei of thorium and helium. Then,

(1) the helium nucleus has more kinetic energy than the thorium nucleus

(2) the helium nucleus has less momentum than the thorium nucleus

(3) the helium nucleus has more momentum than the thorium nucleus

(4) the helium nucleus has less kinetic energy than the thorium nucleus

The binding energy per nucleon of  ${}_3{}^7\mathrm{Li}$and ${}_2{}^4\mathrm{He}$nuclei are 5.60meV and 7.06meV, respectively. 
In the nuclear reaction ${}_3{}^7\mathrm{Li} + {}_1{}^1\mathrm{H} \to {}_2{}^4\mathrm{He} + {}_2{}^4\mathrm{He} + \mathrm{Q}$  , the value of energy Q released is -

(a)19.6MeV

(b)-2.4MeV

(c)8.4MeV

(d)17.3MeV

A radioisotope X with a half-life 1.4x10⁹ yr decays into Y which is stable. A sample of the rock from a cave was found to contain X and Y in the ratio 1:7. The age of the rock is

(1)1.96x10⁹ yr

(2)3.92x10⁹ yr

(3)4.20x10⁹ yr

(4)8.40x10⁹ yr

A certain mass of hydrogen is changed to helium by the process of fusion. The mass defect in the fusion reaction is 0.02866 u. The energy liberated per nucleon is: (given 1 u = 931 MeV)

(1) 2.67 MeV
 

(2) 26.7 MeV
 

(3) 6.675 MeV
 

(4) 13.35 MeV

If the nuclear radius of ${}_{27}Al$ is 3.6 Fermi, the approximate nuclear radius of ${}_{64}Cu$ in Fermi is

(a)2.4                                         (b)1.2

(c)4.8                                         (d)3.6

A mixture consists of two radioactive materials $A_1$ and $A_2$ with half lives of 20 s and 10 s respectively.Initially the mixture has 40g of $A_1$ and 160g of $A_2$. The amount of the two in the mixture will become equal after

(a)60 s                                      (b)80 s

(c)20 s                                      (d) 40 s

The half-life of a radioactive nucleus is 50 days. The time interval $({\mathrm{t}}_2-{\mathrm{t}}_1)$ between the time ${\mathrm{t}}_2$ when $\frac{2}{3}$ of it has decayed and the time ${\mathrm{t}}_1$ when $\frac{1}{3}$ of it had decayed is:

1. 30 days

2. 50 days

3. 60 days

4. 15 days

Fusion reaction takes place at high temperature because

(1) atoms get ionised at high temperature 

(2) kinetic energy is high enough to overcome the Coulomb repulsion between nuclei

(3) molecules break up at high temperature

(4) nuclei break up at high temperature