We are given the following atomic masses:
\({ }_{92}^{238} \mathrm{U}=238.05079~\text{u},{ }_2^4 \mathrm{He}=4.00260~\text{u} \\ { }_{90}^{234} \mathrm{Th}=234.04363~\text{u},{ }_1^1 \mathrm{H}=1.00783~\text{u}\\ { }_{91}^{237} \mathrm{~Pa}=237.05121~\text{u} \)
Here the symbol \(\mathrm{Pa}\) is for the element protactinium \((Z=91)\).
The energy released during the alpha decay of \({}^{238}_{92}\mathrm{U}\) is:
1. \(6.14~\text{MeV}\)
2. \(7.68~\text{MeV}\)
3. \(4.25~\text{MeV}\)
4. \(5.01~\text{MeV}\)

We are given the following atomic masses:
\({ }_{92}^{238} \mathrm{U}=238.05079~\text{u},{ }_2^4 \mathrm{He}=4.00260~\text{u} \\ { }_{90}^{234} \mathrm{Th}=234.04363~\text{u},{ }_1^1 \mathrm{H}=1.00783~\text{u}\\ { }_{91}^{237} \mathrm{~Pa}=237.05121~\text{u} \)
Here the symbol Pa is for the element protactinium \((Z=91)\).
Then:

The energy required in \(\text{MeV/c}^2 \) to separate \({ }_8^{16} \mathrm{O}\) into its constituents is:
(Given: mass defect for \({ }_8^{16} \mathrm{O}=0.13691~ \text{amu}\))

The half-life of ${}_{92}{}^{238}\mathrm{U}$ undergoing $\mathrm{\alpha }$-decay is $4.5\times {10}^9$ years. What is the activity of the 1g sample of ${}_{92}{}^{238}\mathrm{U}$?

1. $2.11\times {10}^4<mspace\; width="1em"></mspace>Bq$

2. $3.12\times {10}^3<mspace\; width="1em"></mspace>Bq$

3. $1.23\times {10}^4<mspace\; width="1em"></mspace>Bq$

4. $2.38\times {10}^3<mspace\; width="1em"></mspace>Bq$

Tritium has a half-life of 12.5 y undergoing beta decay. What fraction of a sample of pure tritium will remain undecayed after 25 y?
 

$1.<mspace\; width="1em"></mspace>\frac{1}{8}\mathrm{th}$
$2.<mspace\; width="1em"></mspace>\frac{1}{4}\mathrm{th}$
$3.<mspace\; width="1em"></mspace>\frac{1}{3}\mathrm{rd}$
$4.<mspace\; width="1em"></mspace>\frac{1}{5}\mathrm{th}$

Which one of the following is incorrect?

Graph given below shows the variation of binding energy per nucleon, E_bn as a function of mass number. For nuclei with mass number A such that, 30 < A < 170, E_bn is almost constant because nuclear forces are:

1. Short-ranged 

2. Medium-ranged

3. Long-ranged

4. None of the above

Graph gives the variation of potential energy of a pair of nucleons as a function of their separation, r. From the graph it can be concluded that the force between nucleons is attractive for distances:

1. Less than r_o

2. Greater than r_o

3. Less than $\frac{r_o}{2}$

4. Less than $\frac{r_o}{4}$

The graph shows the exponential decay of a radioactive specie. The number of nuclei decayed after time t is:

$1.<mspace\; width="1em"></mspace>N_o{e}^{-\lambda t}$
$2.<mspace\; width="1em"></mspace>2N_o{e}^{-\lambda t}$
$3.<mspace\; width="1em"></mspace>N_o-N_o{e}^{-\lambda t}$
$4.<mspace\; width="1em"></mspace>2N_o-N_o{e}^{-\lambda t}$

A nucleus with mass number \(240\) breaks into fragments each of mass number \(120.\) The binding energy per nucleon of unfragmented nuclei is \(7.6~\text{MeV}\) while that of fragments is \(8.5~\text{MeV}.\) The total gain in the binding energy in the process is:
1. \(804~\text{MeV}\)
2. \(216~\text{MeV}\)
3. \(0.9~\text{MeV}\)
4. \(9.4~\text{MeV}\)