Half-life of a radioactive substance is 12.5 h and its mass is 256 g. After what time, the amount of remaining substance is 1 g? [2001]

1. 75 h

2. 100 h 

3. 125 h

4. 150 h

A radioactive substance disintegrates 1/64 of initial value in 60 s. The half-life of this substance is

1. 5 s 

2. 10 s

3. 30 s 

4. 20 s

The nucleus ${}_6{}^{12}C$ absorbs an energetic neutron and emits a beta particle $\left({\beta }^{-}\right)$. The resulting nucleus is 

1. ${}_7{}^{14}C$

2. ${}_7{}^{13}N$ 

3. ${}_5{}^{13}B$ 

4. ${}_6{}^{13}C$

If in a nuclear fusion  process, the masses of the fusion nuclei be $m_1 and m_2$ and the mass of the resultant nucleus be $m_3$, then [2004]

1. $m_3=m_1+m_2$

2. $m_3=\left|m_1-m_2\right|$

3. $m_3<\left(m_1+m_2\right)$ 

4. $m_3>\left(m_1+m_2\right)$

The nuclei of which one of the following pairs of nuclei are isotones? [2005]

1. ${}_{34}S{e}^{74}, {}_{31}G{a}^{71}$ 

2. ${}_{42}M{o}^{92}, {}_{40}Z{r}^{92}$

3. ${}_{38}S{r}^{84}, {}_{38}S{r}^{86}$ 

4. ${}_{20}C{a}^{40}, {}_{16}S_{32}$

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 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