We are given the following atomic masses:

${}_{92}{}^{238}\mathrm{U}$ = 238.05079 u, ${}_2{}^4\mathrm{He}$= 4.00260 u

${}_{90}{}^{234}\mathrm{Th}$ = 234.04363 u, ${}_1{}^1\mathrm{H}$= 1.00783 u

${}_{91}{}^{237}\mathrm{Pa}$= 237.05121 u

Here the symbol Pa is for the element protactinium (Z = 91).

The energy released during the alpha decay of ${}_{92}{}^{238}\mathrm{U}$ is:

1. 6.14 MeV 

2. 7.68 MeV 

3. 4.25 MeV

4. 5.01 MeV 

We are given the following atomic masses:

${}_{92}{}^{238}\mathrm{U}$ = 238.05079 u, ${}_2{}^4\mathrm{He}$= 4.00260 u

${}_{90}{}^{234}\mathrm{Th}$ = 234.04363 u, ${}_1{}^1\mathrm{H}$= 1.00783 u

${}_{91}{}^{237}\mathrm{Pa}$= 237.05121 u

Here the symbol Pa is for the element protactinium (Z = 91).

Then:

1. ${}_{92}{}^{238}\mathrm{U}$ can not spontaneously emit a proton.

2. ${}_{92}{}^{238}\mathrm{U}$ can spontaneously emit a proton.

3. The Q-value of the process is negative.

4. Both (1) and (3)

The energy required in \(\mathrm{MeV} / \mathrm{c}^2\) to separate \({ }_8^{16} \mathrm{O}\) into its constituents is:
(Given mass defect for \({ }_8^{16} \mathrm{O}=0.13691 \mathrm{u}\))
1. \(127.5\)
2. \(120.0\)
3. \(222.0\)
4. \(119.0\)

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. $2.11\times {10}^4 Bq$

2. $3.12\times {10}^3 Bq$

3. $1.23\times {10}^4 Bq$

4. $2.38\times {10}^3 Bq$

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?
 

$1. \frac{1}{8}\mathrm{th}$
$2. \frac{1}{4}\mathrm{th}$
$3. \frac{1}{3}\mathrm{rd}$
$4. \frac{1}{5}\mathrm{th}$

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:

$1. N_o{e}^{-\lambda t}$
$2. 2N_o{e}^{-\lambda t}$
$3. N_o-N_o{e}^{-\lambda t}$
$4. 2N_o-N_o{e}^{-\lambda t}$

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