If there are N nuclear particles in a nucleus of radius R then the number of nuclear particles in radius 3R will be?

Education Journalist | Study Abroad Lead

The number of nuclear particles in a nucleus is proportional to the volume of the nucleus. The volume of a sphere is given by:

V = (4/3)πr³

where r is the radius of the sphere.

If we assume that the nuclear particles are evenly distributed throughout the nucleus, then the number of nuclear particles is proportional to the volume of the nucleus. So, if there are N nuclear particles in a nucleus of radius R, then the number of nuclear particles in a nucleus of radius 3R would be proportional to the volume of the nucleus with a radius of 3R. The volume of a sphere with a radius of 3R is:

V = (4/3)π(3R)³

V = 27(4/3)πR³

So, the number of nuclear particles in a nucleus of radius 3R would be N' =

N' = N × (27(4/3)πR³)/(4/3)πR³

Simplifying, we get:

N' = 27N

Therefore, the number of nuclear particles in a nucleus of radius 3R would be 27 times the number of nuclear particles in a nucleus of radius R, assuming that the particles are evenly distributed throughout the nucleus.

Read More:

Related Topics
Nuclear Physics	Nuclear reactor based on nuclear fission	Nucleon
Mass Energy Equivalence	Atoms and Nuclei Important Questions	Nuclear Binding Energy
Nuclei	Mass-Energy and Nuclear Binding Energy	Radioactive Decay Formula

CBSE CLASS XII Related Questions

1.
An electric field $\vec{E}$ is established across the ends of a cylindrical conductor of length L and area of cross-section A. Discuss how electrons attain an average velocity, independent of time. Hence, obtain a relation between current in the conductor and this ‘average velocity’ of electrons.

View Solution

2.
Capacitors are manufactured with certain standard capacitances and working voltages. However, these standard values may not be the ones that are actually needed in a particular application. Two or more capacitors can be grouped in series or in parallel to achieve desired capacitance and voltage. When connected in series, the total capacitance decreases while the voltage rating increases, whereas in parallel connections, the total capacitance increases and maintains the same voltage rating. A capacitor stores energy in the electric field between its plates and stored energy is proportional to the square of the voltage and capacitance $U = \frac{1}{2}CV^2$, where symbols have their usual meanings.
Two capacitors, one of $3 \ \mu$F and the other of $6 \ \mu$F, are connected in series in the circuit as shown in the figure, for a long time. }

3.
The resistance of a metal wire at $ 20^\circ \text{C} $ is $ 1.05 \, \Omega $ and at $ 100^\circ \text{C} $ is $ 1.38 \, \Omega $. Determine the temperature coefficient of resistivity of this metal.

View Solution

4.
A student sets up the circuit as shown in the figure to find the value of unknown resistance X and records a set of readings of the voltmeter and the ammeter by using the rheostat.

5.
Read the following paragraph and answer the questions that follow.
A p-type or n-type semiconductor can be converted into a p-n junction by doping it with suitable impurity. The motion of majority charge carriers causes diffusion current across the junction while the barrier electric field causes motion of minority carriers for drift current. In case of unbiased diode, the diffusion and drift currents are equal. This equilibrium is disturbed by the biasing batteries. Diodes, therefore, allow currents in one direction. This property of diode is used in making rectifiers.

6.
Two metal spheres of radii $r_1$ and $r_2$ ($> r_1$) having charges $q_1$ and $q_2$ respectively kept in air, are brought in contact. Which of the following statements is not correct ?

The total charge of the two spheres is conserved.
Both spheres attain the same potential.
The final potential of the system equals $\frac{1}{4\pi\epsilon_0} \frac{(q_1 + q_2)}{(r_1 + r_2)}$
The final potential of the system equals $\frac{1}{4\pi\epsilon_0} \frac{(q_1 + q_2) (r_1 + r_2)}{r_1 r_2}$

View Solution

If there are N nuclear particles in a nucleus of radius R then the number of nuclear particles in radius 3R will be?

CBSE CLASS XII Related Questions

3.
The resistance of a metal wire at \( 20^\circ \text{C} \) is \( 1.05 \, \Omega \) and at \( 100^\circ \text{C} \) is \( 1.38 \, \Omega \). Determine the temperature coefficient of resistivity of this metal.

4.
A student sets up the circuit as shown in the figure to find the value of unknown resistance X and records a set of readings of the voltmeter and the ammeter by using the rheostat.

6.
Two metal spheres of radii $r_1$ and $r_2$ ($> r_1$) having charges $q_1$ and $q_2$ respectively kept in air, are brought in contact. Which of the following statements is not correct ?

Similar Physics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

If there are N nuclear particles in a nucleus of radius R then the number of nuclear particles in radius 3R will be?

CBSE CLASS XII Related Questions

3. The resistance of a metal wire at \( 20^\circ \text{C} \) is \( 1.05 \, \Omega \) and at \( 100^\circ \text{C} \) is \( 1.38 \, \Omega \). Determine the temperature coefficient of resistivity of this metal.

4.A student sets up the circuit as shown in the figure to find the value of unknown resistance X and records a set of readings of the voltmeter and the ammeter by using the rheostat.

6.Two metal spheres of radii $r_1$ and $r_2$ ($> r_1$) having charges $q_1$ and $q_2$ respectively kept in air, are brought in contact. Which of the following statements is not correct ?

Similar Physics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

3.
The resistance of a metal wire at \( 20^\circ \text{C} \) is \( 1.05 \, \Omega \) and at \( 100^\circ \text{C} \) is \( 1.38 \, \Omega \). Determine the temperature coefficient of resistivity of this metal.

4.
A student sets up the circuit as shown in the figure to find the value of unknown resistance X and records a set of readings of the voltmeter and the ammeter by using the rheostat.

6.
Two metal spheres of radii $r_1$ and $r_2$ ($> r_1$) having charges $q_1$ and $q_2$ respectively kept in air, are brought in contact. Which of the following statements is not correct ?