Nuclear Stability

Q. The mass defect in a nucleus is $3.5\text{amu}$. Then the binding energy of the nucleus is

1. $3.258\text{MeV}$
2. $32.58\text{MeV}$
3. $325.8\text{MeV}$
4. $3260.25\text{MeV}$

Q.

The formula $\mathrm{R}=(1.310–15){\mathrm{A}}^{1/3}\mathrm{m}$ can be used to calculate the radius $\mathrm{R}$ of a nucleus with mass number $\mathrm{A}$. As a result, a nucleus mass density is on the order of: $({\mathrm{M}}_{\mathrm{prot}}={\mathrm{M}}_{\mathrm{neut}}=1.67\times {10}^{-27}\mathrm{kg})$

1. ${10}^{17}\mathrm{kg}{\mathrm{m}}^{-3}$

2. ${10}^{10}\mathrm{kg}{\mathrm{m}}^{-3}$

3. ${10}^{24}\mathrm{kg}{\mathrm{m}}^{-3}$

4. ${10}^3\mathrm{kg}{\mathrm{m}}^{-3}$

Q. If $F_{p-p},F_{p-n},F_{n-n}$ are nuclear forces between two protons, a proton and a neutron and two neutrons respectively inside a nucleus, then

1. $F_{p-p}<F_{p-n}<F_{n-n}$
   
2. $F_{p-p}=F_{p-n}=F_{n-n}$
   
3. $F_{p-p}<F_{p-n}=F_{n-n}$
   
4. $F_{p-p}>F_{p-n}=F_{n-n}$
   

Q.

What is the range of all four forces of nature? (viz, gravitational force , strong neuclear , weak nuclear force, and electromagnetic force)

Q. An electron of mass $m$ and charge $e$ initially at rest gets accelerated by a constant electric field $E.$ The rate of change of de-Broglie wavelength of this electron at time $t,$ is (ignore the relativistic effects)

1. $\frac{-h}{eE{t}^2}$
2. $\frac{-eht}{E}$
3. $\frac{mh}{eE{t}^2}$
4. $\frac{h}{eE}$

Q.

Why nuclear density is not dependent on the mass number?

Q. A photon can be deflected by -

1. Only electric field
2. Only magnetic field
3. Both electric and magnetic field
4. Neither by electric field nor by magnetic field

Q. For a nucleus to be stable, the correct relation between neutron number N and Proton number Z is

1. $N>Z$
   
2. $N=Z$
   
3. $N<Z$
   
4. $N\ge Z$

Q. When the number of nucleons in a nucleus increases the binding energy per nucleon-

1. Remains constant with increase in mass number
2. Increase continuously with increase in mass number
3. Decrease continuously with increase in mass number
4. First increases and then decreases with increase in mass number.

Q. $\text{Assertion}$ : Electron capture occurs more often than positron emission in heavy elements.
$\text{Reason}$ : Heavy elements exhibit radioactivity.
Read the assertion and reason carefully to mark the correct option out of the options given below:

1. Both assertion and reason are true and the reason is the correct explanation of the assertion.
2. Both assertion and reason are true but reason is not the correct explanation of the assertion.
3. Assertion is true but reason is false.
4. Assertion is false but reason is true.

Q. The impact parameter $\left(b\right)$ is proportional to -

$\theta$ is scattering angle.

1. $\cot \left(\theta /2\right)$
2. $\tan \left(\theta /2\right)$
3. $\cot \left(\theta \right)$
4. $\tan \left(\theta \right)$

Q.

${}^{131}I$ is an isotope of Iodine that $\beta -$ decays to an isotope of Xenon with a half-life of $8\text{days}$. A small amount of a serum labelled with ${}^{131}I$ is injected into the blood of a person. The activity of the amount of ${}^{131}I$ injected was $2.4\times {10}^5\text{Becquerel (Bq)}$. It is known that the injected serum will get distributed uniformly in the blood stream in less than half an hour. After $11.5\text{hours},2.5\text{ml}$ of blood is drawn from the person's body, and gives an activity of $115\text{Bq}$. The total volume of blood in the person's body, in $\text{liters}$ is approximately _______.

Q. The binding energies per nucleon are $5.3\text{MeV},6.2\text{MeV}$ and $7.4\text{MeV}$ for the nuclei with mass numbers $3,4$ and $5$ respectively. If one nucleus of mass number $3$ combines with one nucleus of mass number $5$ to give two nuclei of mass number $4$, then

1. $3.3\text{MeV}$ of energy is absorbed.
2. $0.3\text{MeV}$ of energy is released.
3. $0.3\text{MeV}$ of energy is absorbed.
4. $3.3\text{MeV}$ of energy is released.

Q. In most stable nuclei, neutron number $N$ and proton number $Z$ has the relation

1. $N=Z$
2. $N>Z$
3. $N<Z$
4. $N⩾Z$

Q.

If the N/Z ratio of an atom is less than 1 then the nuclide is said to be stable. Here 'N' is the number of neutrons and 'Z' is the atomic number. Which of the following nuclides is stable?

1. ${}^{3}He$
2. ${}^{1}H$
3. ${}^{3}He$ and ${}^{1}H$
4. None of these

Q.

Describe how contact force like friction etc as well as chemical reaction are instances of electromagnetic force

Q. Binding energy per nucleon versus mass number curve for nuclei is shown in the figure. $\text{W, X, Y}$ and $\text{Z}$ are four nuclei indicated on the curve. The process that would release energy is

1. $Y\to 2Z$
2. $W\to X+Z$
3. $X\to Y+Z$
4. $W\to 2Y$

Q. Mass defect of a nucleus refers to -

1. Error in the measurement of atomic masses.
2. Packing fraction of the atom.
3. Increase in mass over local mass of its constituents to bind the atoms.
4. Mass annihilated to produce energy to bind the nucleons.

Q. The nuclear reaction ${}_{48}{\text{Cd}}^{107}\to {}_{47}{\text{Ag}}^{107}$ can occur with the

1. $\alpha$ $\text{decay}$
2. ${\beta }^{-}$ $\text{decay}$
3. $\text{Proton emission}$
4. $\text{Electron capture}$

Q. If three ${}^{4}He$ nuclei combine to form a ${}^{12}C$ nucleus, energy is liberated. Why can't helium nuclei combine on their own and minimize the energy?

1. He gas is rare, so collisions between nuclei are also rare;
2. It happens and the we see in nature was formed by this method only in Earth's atmosphere;
3. The strong nuclear force between nucleons is attractive but short range; the Coulomb force between protons is long range, but repulsive;

Q. A heavy nucleus having a mass number $200$ gets disintegrated into two small fragments of mass numbers $80$ and $120$. If binding energy per nucleon for perent atom is $6.5$ MeV and for daughter nuclei is $7$ MeV and $8$ MeV respectively, then the energy released in the decay will be :

1. $200MeV$
2. $-220MeV$
3. $220MeV$
4. $180MeV$

Q. The binding energies of nuclei $X$ and $Y$ are $E_1$ and $E_2$ respectively. Two atoms of $X$ fuse to give one atom of $Y$ and an energy $Q$ is released. Then

1. $Q=2E_1-E_2$
2. $Q=E_2-2E_1$
3. $Q=2E_1+E_2$
4. $Q=2E_2+E_1$

Q. In stable nuclei the number of protons $\left(Z\right)$ and number of neutrons $\left(N\right)$ are related as

1. $N$ = $Z$
2. $N$ > $Z$
3. $N$ <$Z$
4. $N$ = $Z$ = $0$

Q. An ionized gas contains both positive and negative ions. If it is subjected simultaneously to an electric field along the $+$ X direction and a magnetic field along the $+$ Z direction, then :

1. Positive ions deflect towards $+$ Y direction and negative ions towards $-$ Y direction
2. All ions deflect towards $+$ Y direction
3. All ions deflect towards $-$ Y direction
4. Positive ions deflect towards $-$ Y direction and negative ions towards $+$ Y direction

Q. (a) Derive the mathematical expression for law of radioactive decay for a sample of a radioactive nucleus.
(b) How is the mean life of a given radioactive nucleus related to the decay constant?

Q. The wavelengths of $K_{\alpha }$ X-rays for lead isotopes $P{b}^{208},P{b}^{206}$ and $P{b}^{204}$ are ${\lambda }_1,{\lambda }_2$ and ${\lambda }_3$ respectively. Then

1. ${\lambda }_2=\sqrt{{\lambda }_1{\lambda }_3}$
2. ${\lambda }_2={\lambda }_1+{\lambda }_3$
3. ${\lambda }_2={\lambda }_1{\lambda }_3$
4. ${\lambda }_2=\frac{{\lambda }_1}{{\lambda }_3}$

Q. The mass defect for helium nucleus is $0.0304$ $a.m.u$. The binding energy per nucleon of helium nucleus is ________

1. $28.3$ $MeV$
2. $7.075$ $MeV$
3. $9.31$ $MeV$
4. $200$ $MeV$

Q.

The high density of the nucleus suggests

1. compactness of the nucleus

2. hollowness of the nucleus

3. large number of nucleous

4. none of these

Q. Binding energy per nucleon vs mass number curve for nuclei is shown in the figure. W, X, Y and Z are four nuclei as indicated on the curve. The process that would release energy is–

1. $Y\to 2Z$
2. $W\to Y+Z$
3. $W\to 2Y$
4. $X\to Y+Z$

Q. Which of the following particles are not deflected in an electric or a magnetic fields?

1. alpha
2. beta
3. gamma
4. all the above