The count rate of a Geiger Muller counter for the radiation of a radioactive material of half-life 30 min decreases to 5 $s^{-1}$ after 2 h. The initial count rate was [1995]

1. 20 $s^{-1}$ 

2. 25 $s^{-1}$ 

3. 80 $s^{-1}$ 

4. 625 $s^{-1}$

An element A decays into element C by a two step process

$A\to B+{}_{2}H{e}^4$
$B\to C+2e^{-}$

then  [1989]

1. A and C are isotopes

2. A and C are isobars

3. A and B are isotopes

4. A and B are isobars

The radius R of a nuclear matter varies with A as

1. $R \alpha A^{2/3}$

2. $R \alpha A^{1/3}$

3. $R \alpha A^0$ 

4. $R \alpha A$

Number of nuclei of a radioactive substance at time t = 0 are 2000 and 1800 at time t = 2s. Number of nuclei left after t = 6s is [MGIMS 2010]

1. 1442 

2. 1554 

3. 1652 

4. 1458

In a radioactive material, the activity at time $t_1$ is $R_1$ and at a later time, $t_2$ is $R_2$. If the decay constant of the material is $\lambda$, then:

1. $R_1=R_2{e}^{-\lambda \left(t_1-t_2\right)}$   

2. $R_1=R_2{e}^{\lambda \left(t_1-t_2\right)}$

3. $R_1=R_2\left(\frac{t_2}{t_1}\right)$ 

4. $R_1=R_2$

Which of the following are suitable for the fusion process ? [2002]

1. Light nuclei

2. Heavy nuclei

3. Elements lying in the middle of periodic table

4. Elements lying in the middle of binding energy curve

In the nuclear reaction: $X{(n,}_{}$ $\alpha )3L{i}^7$, the term X will be:

1. ${}_{5}B_{10}$ 

2. ${}_{5}B_9$

3. ${}_{5}B_{11}$

4. ${}_{2}H{e}^4$

Two radioactive substances A and B have decay constants $5\lambda$ and $\lambda$ respectively. At t=0 they have the same number of nuclei. The ratio of number of nuclei of A to those of B will be ${\left(\frac{1}{e}\right)}^2$ after a time interval

1. $\frac{1}{4\lambda }$   

2. $4\lambda$

3. $2\lambda$ 

4. $\frac{1}{2\lambda }$

10 g of radioactive material of half-life 15 year is kept in store for 20 years. The disintegrated material mass is [Pb. PMT 2002]

1. 12.5 g

2. 10.5 g

3. 6.03 g

4. 4.03 g

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