# The activity of a radioactive sample is measured as 9750 counts/min at t = 0 and as 975 counts/min at t = 5 min. The decay constant is approximately: 1. 0.922/min            2. 0.691/min          3. 0.461/min            4. 0.230/min

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The energy equivalent of one atomic mass unit is:

1. $1.6×{10}^{-19}$ $J$

2. $6.02×{10}^{23}$ $J$

3. 931 MeV

4. 9.31 MeV

Subtopic:  Mass-Energy Equivalent |
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Solar energy is due to:

1. fusion reaction.

2. fission reaction.

3. combustion reaction.

4. chemical reaction.

Subtopic:  Nuclear Energy |
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At time t = 0, N1 nuclei of decay constant λ1 and N2 nuclei of decay constant λ2 are mixed. The decay rate of the mixture is:

1. $-{N}_{1}{N}_{2}{e}^{-\left({\lambda }_{1}+{\lambda }_{2}\right)t}$ 

2. $-\left(\frac{{N}_{1}}{{N}_{2}}\right)$ ${e}^{{}^{-\left({\lambda }_{1}+{\lambda }_{2}\right)t}}$ 

3. $-\left({N}_{1}{\lambda }_{1}{e}^{-{\lambda }_{1}t}\right)$ $+$ ${N}_{2}{\lambda }_{2}{e}^{-{\lambda }_{2}t}$ 

4. $-{N}_{1}{\lambda }_{1}{N}_{2}{\lambda }_{2}{e}^{{}^{-\left({\lambda }_{1}+{\lambda }_{2}\right)t}}$

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A nucleus ${}_{n}{}^{m}X$ emits one $\alpha$ and two $\beta -$particles. The resulting nucleus is

1. ${}_{n}{}^{m-4}X$

2. ${}_{n-2}{}^{m-4}X$

3. ${}_{n-4}{}^{m-4}X$

4. None of these

Subtopic:  Types of Decay |
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The half-life period of a radioactive substance is 6 h.  If after 24 h, activity is 0.01 $\mu$Ci, what was the initial activity?

1. 0.04 $\mu$Ci

2. 0.08 $\mu$Ci

3. 0.24 $\mu$Ci

4. 0.16 $\mu$Ci

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The radius of a nucleus of a mass number A is directly proportional to [MH CET 1999; AMU (En.) 2001; UPSEAT 2004; DUMET 2010]

1. ${A}^{3}$

2. A

3. ${A}^{2/3}$

4. ${A}^{1/3}$

Subtopic:  Nuclear Binding Energy |
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${m}_{P}$ and ${m}_{n}$ are masses of proton and neutron respectively. An element of mass m has Z protons and N neutrons, then

1. $m>Z{m}_{p}+N{m}_{n}$

2. $m=Z{m}_{p}+N{m}_{n}$

3. $m

4. m may be greater than, less than or equal to $Z{m}_{p}+N{m}_{n}$, depending on the nature of the element.

Subtopic:  Mass-Energy Equivalent |
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The nuclei  can be described as [1990]

1. isotones

2. isobars

3. isotopes of carbon

4. isotopes of nitrogen

Subtopic:  Mass-Energy Equivalent |
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The radioactivity of a sample is ${A}_{1}$ at a time ${t}_{1}$ and ${A}_{2}$ at time ${t}_{2}$.  If the mean life of the specimen is T, the number of atoms that have disintegrated in the time interval of ${t}_{2}-{t}_{1}$ is:

1. ${A}_{1}-{A}_{2}$

2. $\frac{{A}_{1}-{A}_{2}}{T}$

3. $\left({A}_{1}-{A}_{2}\right)T$

4. ${A}_{1}{t}_{1}-{A}_{2}{t}_{2}$