Question:
Choose the correct statement of the following
Choose the correct statement of the following
Show Hint
Remember:
\[
R=R_0A^{1/3}
\]
Since nuclear volume and nuclear mass both vary proportionally with \(A\), nuclear density remains nearly constant for all nuclei.
Updated On: Jun 22, 2026
- The nuclear density in general, is independent of mass number \(A\).
- The radius of a nucleus is directly proportional to the mass number \(A\) of the nucleus.
- The binding energy of a nucleus is inversely proportional to its mass defect.
- Energy is absorbed when heavy nuclei undergo transmutation into light nuclei.
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Analyze option (1).
The radius of a nucleus is given by \[ R=R_0A^{1/3} \] The volume of the nucleus is therefore \[ V=\frac{4}{3}\pi R^3 \] Substituting \(R=R_0A^{1/3}\), \[ V\propto (A^{1/3})^3 \] \[ V\propto A \] The mass of the nucleus is also proportional to \(A\).
Hence, \[ \text{Density}=\frac{\text{Mass}}{\text{Volume}} \] Since both mass and volume are proportional to \(A\), \[ \text{Density}=\text{constant} \] Therefore, nuclear density is approximately independent of mass number \(A\).
Thus, option (1) is correct.
Step 2: Analyze option (2).
The radius of a nucleus is not directly proportional to \(A\).
Instead, \[ R\propto A^{1/3} \] Hence, option (2) is incorrect.
Step 3: Analyze option (3).
Binding energy is directly proportional to mass defect according to Einstein’s relation: \[ E=\Delta mc^2 \] Thus, larger mass defect means larger binding energy.
Therefore, binding energy is not inversely proportional to mass defect.
Hence, option (3) is incorrect.
Step 4: Analyze option (4).
When heavy nuclei split into lighter nuclei during nuclear fission, energy is released, not absorbed.
This happens because the binding energy per nucleon increases for medium mass nuclei.
Hence, option (4) is incorrect.
Step 5: Final conclusion.
Therefore, the correct statement is \[ \boxed{\text{The nuclear density in general is independent of mass number }A} \]
The radius of a nucleus is given by \[ R=R_0A^{1/3} \] The volume of the nucleus is therefore \[ V=\frac{4}{3}\pi R^3 \] Substituting \(R=R_0A^{1/3}\), \[ V\propto (A^{1/3})^3 \] \[ V\propto A \] The mass of the nucleus is also proportional to \(A\).
Hence, \[ \text{Density}=\frac{\text{Mass}}{\text{Volume}} \] Since both mass and volume are proportional to \(A\), \[ \text{Density}=\text{constant} \] Therefore, nuclear density is approximately independent of mass number \(A\).
Thus, option (1) is correct.
Step 2: Analyze option (2).
The radius of a nucleus is not directly proportional to \(A\).
Instead, \[ R\propto A^{1/3} \] Hence, option (2) is incorrect.
Step 3: Analyze option (3).
Binding energy is directly proportional to mass defect according to Einstein’s relation: \[ E=\Delta mc^2 \] Thus, larger mass defect means larger binding energy.
Therefore, binding energy is not inversely proportional to mass defect.
Hence, option (3) is incorrect.
Step 4: Analyze option (4).
When heavy nuclei split into lighter nuclei during nuclear fission, energy is released, not absorbed.
This happens because the binding energy per nucleon increases for medium mass nuclei.
Hence, option (4) is incorrect.
Step 5: Final conclusion.
Therefore, the correct statement is \[ \boxed{\text{The nuclear density in general is independent of mass number }A} \]
Was this answer helpful?
0
0
Top AP EAPCET Physics Questions
- A body is projected from the ground at an angle of $\tan^{-1} \left( \frac{8}{7}\right)$ with the horizontal. The ratio of the maximum height attained by it to its range is
- A lens forms real and virtual images of an object, when the object is at $u_{1}$ and $u_{2}$ distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (take, the magnification of the real image as $m$ )
- Two spheres $P$ and $Q$, each of mass $200\, g$ are attached to a string of length one metre as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that of between $P$ and $O$ is $(P$ is at mid-point of the line joining $O$ and $Q$ )
- The radii of the two columns in a U - tube are r1 and r2. When a liquid of density p (angle of contact is $ 0{}^\circ $ ) is filled in it, the level difference of the liquid in the two arms is h. The surface tension of the liquid is: (g = acceleration due to gravity)
- A rigid metallic sphere is spinning around its own axis in the absence of external torque. If the temperature is raised, its volume increases by $9 \%$. The change in its angular speed is
View More Questions
Top AP EAPCET Nuclei Questions
- Choose the correct statement regarding nuclear properties:
- An ancient artifact retains 75% of its original carbon-14. Given $ T_{1/2} = 5730 \, \text{years} $, and $ \ln(0.5) = -0.7 $, $ \ln(0.75) = -0.3 $, find the age of the sample.
- Binding energy per nucleon of deuteron and Helium nuclei are 1.1 MeV and 7 MeV respectively. If a single Helium nucleus was formed by adding two Deuterons, the energy released is
- Energy released in the fission of a single \( {}_{92}\text{U}^{235} \) nucleus is 200 MeV. The fission rate of a \( {}_{92}\text{U}^{235} \) fueled reactor operating at a power level of 5W is:
- In a nuclear reactor, heavy water (D_2O) is used as a moderator. Its main function is to:
View More Questions
Top AP EAPCET Questions
- A body is projected from the ground at an angle of $\tan^{-1} \left( \frac{8}{7}\right)$ with the horizontal. The ratio of the maximum height attained by it to its range is
- The four quantum numbers of the valence electron of potassium are :
- A lens forms real and virtual images of an object, when the object is at $u_{1}$ and $u_{2}$ distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (take, the magnification of the real image as $m$ )
- Two spheres $P$ and $Q$, each of mass $200\, g$ are attached to a string of length one metre as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that of between $P$ and $O$ is $(P$ is at mid-point of the line joining $O$ and $Q$ )
- The volume of $0.02\, M$ acidified permanganate solution required for complete reaction of $60\, mL$ of $0.01\, MI^{-}$ ion solution to form $I_2$ in $mL$ is
View More Questions