The counting rate observed from a radioactive source at t = 0 second was 1600 counts per second and at t = 8 seconds it was 100 counts per second. The counting rate observed, as counts per second, at t = 6 seconds will be:

1. 400

2. 300

3. 200

4. 150

If $N_0$ is the original mass of the substance of half life period $T_{1/2}$= 5 years, then the amount of substance left after 15 years is [AIEEE 2012]

1. $N_0$/8 

2. $N_0$/16

3. $N_0$/2

4. $N_0$/4

The mass number of He is 4 and that for sulphur is 32. The radius of sulphur nucleus is larger than that of helium, by times [J & K CET 2010]

1. $\sqrt{8}$ 

2. 4

3. 2 

4.  8

The numbers of nuclei of a radioactive substance at time t = 0 are 1000 and 900 at time t = 2 sec. Then the number of nuclei at time t = 4 sec will be:

1. 800

2. 810 

3. 790 

4. 700

A nucleus ${}_Z{}^{A}X$ has mass represented by m(A, Z). If $m_p$ and $m_n$ denote the mass of proton and neutron respectively and BE is the binding energy (in MeV), then:
[2007]

1. BE = [m(A, Z) - Z$m_p$- (A - Z)$m_n$] $c^2$

2. BE = [Z$m_p$+ (A - Z)$m_n$- m(A,Z)] $c^2$

3. BE = [Z$m_p$+ A$m_n$- m(A, Z)] $c^2$

4. BE = m(A, Z) - Z$m_p$- (A, Z)$m_n$

Half-lives of two radioactive substances A and B respectively are 20 min and 40 min.  Initially, the samples of A and B have an equal number of nuclei. After 80 min the ratio of the remaining number of A and B nuclei is:

1. 1 : 16

2. 4 : 1

3. 1 : 4 

4. 1 : 1

Radioactive ${}_{27}{}^{60}Co$ is transformed into stable ${}_{28}{}^{60}Ni$ by emitting two $\gamma$-rays of energies

1. 1.33 MeV and 1.17 MeV in succession

2. 1.17 MeV and 1.33 MeV in succession

3. 1.37 MeV and 1.13 MeV in succession

4. 1.17 MeV and 1.13 MeV in succession

The volume occupied by an atom is greater than the volume of the nucleus by factor of about [2003]

1. ${10}^{10}$ 

2. ${10}^{15}$ 

3. ${10}^1$ 

4. ${10}^5$

A radioactive nucleus undergoes a series of decay according to the scheme 

$A\stackrel{\alpha }{\to }{A}_1\stackrel{\beta }{\to }{A}_2\stackrel{\alpha }{\to }{A}_3\stackrel{\gamma }{\to }{A}_4$

If the mass number and atomic number of A are 180 and 72 respectively, then what are these number for $A_4$?

1. 172 and 69 

2. 174 and 70

3. 176 and 69

4. 176 and 70

Nuclear fission can be explained by [2000]

1. proton-proton cycle

2. liquid drop model of nucleus

3. independent of nuclear particle model

4. nuclear shell model