Nuclear Radius

Q.

The number of molecules in 8 grams of oxygen gas is ______

Q. A heavy nucleus at rest breaks into two fragments which fly off with velocities in the ratio 8 : 1. The ratio of radii of the fragments is

1. 4 : 1
2. 2 : 1
3. 1 : 2
4. 1 : 4

Q. Obtain approximately the ratio of the nuclear radii of the gold isotope 19779 Au and the silver isotope 10747 Ag .

Q. The potential variation with distance for a uniformly charged ring having radius $R$ and carrying charge $Q$ is:

1. 
2. 
3. 
4. 

Q. The electric potential at the surface of an atomic nucleus $(Z=50)$ of radius $9\times {10}^{-15}\text{m}$ is

1. $80\text{V}$
2. $8\times {10}^6\text{V}$
3. $9\text{V}$
4. $9\times {10}^6\text{V}$

Q.

The graph of $ln\frac{R}{R_0}$ versus ln A (R radius of a nucleus and A - its mass number) is

1. a straight line

2. a parabola

3. an ellipse

4. none

Q.

The density of nuclear matter is:

1. directly proportional to the number of neutrons in the nucleus

2. directly proportional to the number of protons in the nucleus

3. directly proportional to the square of the number of nucleons in the nucleus

4. independent of the number of nucleons in the nucleus

Q. The ratio of radii of nuclei ${}_{13}^{27}$ Al and ${}_{52}^{125}$ Te is approximately

1. 6 : 10
2. 13 : 52
3. 40 : 177
4. 14 : 7

Q.

We are provided with the mass of universe i.e. 10⁵⁵ but the question is how do we measured that because we know that its mucn of the space so how can we measure it?

Q. A system consists of two small spheres of mass $1\text{kg}$ and $2\text{kg}$ interconnected by a weightless spring. At $t=0$, the spheres are set in motion with initial velocities as shown in the figure. The position vector of centre of mass at $t=0$ is $\left(20\hat{j}\right)\text{m}$. Initially, spring is in its natural length. The system moves in earth's gravitational field. The momentum of the system at $t=2\text{s}$ in $\text{kg-m/s}$ is

$[g=10{\text{m/s}}^2,\text{com is initial centre of mass}]$

1. $12\hat{i}-32\hat{j}$
2. $16\hat{i}-64\hat{j}$
3. $18\hat{i}-64\hat{j}$
4. $12\hat{i}-18\hat{j}$

Q. The nuclear charge (Ze) is non-uniformly distribute within a nucleus of radius R. The charge density $\rho \left(r\right)$ [charge per unit volume] is dependent on the radial distance r from the centre of the nucleus as shown in figure. Select correct alternative/s.

1. Electric potential at r=R is proportional to b
2. Electric field at r=R is proportional to a
3. Electric potential at r=R is proportional to a
4. Electric field at r=R is independent of b

Q. From the relation R = R0A1/3, where R0is a constant and A is themass number of a nucleus, show that the nuclear matter density isnearly constant (i.e. independent of A).

Q. Taking the electronic charge as ${}^{\prime }{e}^{\prime }$ and the permittivity as ${}^{\prime }{\epsilon }_0^{\prime }$, use dimenstional analysis to determine the correct expression for ${\omega }_p$

1. $\sqrt{\frac{m{\epsilon }_0}{N{e}^2}}$
2. $\sqrt{\frac{m{\epsilon }_0}{Ne}}$
3. $\sqrt{\frac{Ne}{m{\epsilon }_0}}$
4. $\sqrt{\frac{N{e}^2}{m{\epsilon }_0}}$

Q. Calculate the time taken by the light to pass through a nucleus of diameter$1.3\times {10}^{-15}m$, if the speed of light is $3\times {10}^{8}m/s$.

1. $5.2\times {10}^{-25}s$
2. $4.3\times {10}^{-24}s$
3. $5.2\times {10}^{-24}s$
4. $4.3\times {10}^{-25}s$

Q. Two nuclei have mass number in the ratio 1:2, what is the ratio of their nuclear densities?

Q. Two nuclei have their mass numbers in the ratio of $1:3$. The ratio of their nuclear densities would be

1. $1:3$
2. $3:1$
3. ${\left(3\right)}^{1/3}:1$
4. $1:1$

Q.

Which one of the following statements about the atomic nucleus is accurate?

1. The nucleus is held together mostly by the electrical and gravitational forces

2. All nuclei have nearly the same density

3. Smaller nuclei are denser than larger nuclei

4. Large nuclei are denser than light nuclei

Q.

Imagine a hypothetical fluid made only of helium nuclei (practically, just liquid ionized helium), and let's say, it's seen that it floats on water, like oil. A similar fluid made of uranium${(}_{92}^{238}U)$ nuclei, what will happen to it once put in the same water?

1. It will dissolve in water

2. It will sink below water and settle at the bottom

3. It will float above water, just like in helium's case

4. It's hard to infer from given information.

Q. If the radius of a ${}_{13}^{27}Al$ nucleus is estimated to be $3.6$ fermi, find the radius of a ${}_{52}^{125}Te$ nucleus.

Q. Estimate the proportion of boron impurity which will increase the conductivity of a pure silicon sample by a factor of $100$. Assume that each boron atom creates a hole, and the concentration of holes in pure silicon at the same temperature is $7\times {10}^{15}$ holes per cubic meter. Density of silicon is $5\times {10}^{28}$ atoms per cubic meter.

1. $1.8\times {10}^5$
2. $3.571\times {10}^{10}$
3. $2.580\times {10}^{10}$
4. $4.576\times {10}^{10}$

Q.

The ratio of volume of atom to volume of nucleus is

1. 10¹⁰

2. 10¹⁵

3. 1/1000

4. 10

Q. The radius of ${}_{13}^{27}\text{Al}$ is $3.6$ Fermi. Find the radius of ${}_{52}^{125}\text{Te}$

1. $6$ Fermi
2. $8$ Fermi
3. $4$ Fermi
4. $5$ Fermi

Q. Order of magnitude of density of uranium nucleus is ( $m_p$ = ${1.67\times 10}^{-27}kg$)

1. ${10}^{14}kg/m^3$
2. ${10}^{11}kg/m^3$
3. ${10}^{17}kg/m^3$
4. ${10}^{20}kg/m^3$

Q. The radii of two nuclei with mass numbers $8$ and $64$ is

1. $2:1$
2. $1:2$
3. $2:2$
4. $1:1$

Q. The stable nucleus that has a radius $1/3$ that $O{s}^{189}$ is

1. ${}_3{Li}^7$
2. ${}_2{He}^4$
3. ${}_5{B}^{10}$
4. ${}_6{C}^{12}$

Q. The radius of a nucleus of a mass number A is directly proportional to

1. $A^3$
   
2. $A$
   
3. $A^{\frac{2}{3}}$
   
4. $A^{\frac{1}{3}}$

Q. If radius of the ${}_{13}^{27}Al$ nucleus is taken to be $R_{Al}$, then the radius of ${}_{53}^{125}Te$ nucleus is nearly

1. ${\frac{53}{13}}^{1/3}{R}_{Al}$
2. $\frac{5}{3}{R}_{Al}$
3. $\frac{3}{5}{R}_{Al}$
4. ${\frac{13}{53}}^{1/3}{R}_{Al}$

Q. The ratio of rate of loss of heat by a black body at ${227}^o$C to ${127}^o$C in a surrounding at ${27}^o$C is ____________.

1. $3.108:1$
2. $25:16$
3. $16:1$
4. $2.176:1$

Q. A nucleus at rest splits into two nuclear parts having mass number in the ratio $1:2$. Their velocities are in the ratio

1. $8:1$
2. $6:1$
3. $4:1$
4. $2:1$

Q. Some statement regarding nucleus are given

$\text{(A) Volume is independent of}A$

$\text{(B) Volume is dependent on}{A}^{\frac{1}{3}}$

$\text{(C) Volume is dependent on}A$

$\text{(D) Density is dependent on}A$

$\text{(E) Density is independent of}A$

Here $A$ is atomic mass number, then choose correct option