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

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Jasmine Grover Content Strategy Manager

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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.

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CBSE CLASS XII Related Questions

  • 1.
    A charge \( -6 \mu C \) is placed at the center B of a semicircle of radius 5 cm, as shown in the figure. An equal and opposite charge is placed at point D at a distance of 10 cm from B. A charge \( +5 \mu C \) is moved from point ‘C’ to point ‘A’ along the circumference. Calculate the work done on the charge.
    work done on the charge


      • 2.
        Two conductors A and B of the same material have their lengths in the ratio 1:2 and radii in the ratio 2:3. If they are connected in parallel across a battery, the ratio \( \frac{v_A}{v_B} \) of the drift velocities of electrons in them will be:

          • 2
          • \( \frac{1}{2} \)
          • \( \frac{3}{2} \)
          • \( \frac{8}{9} \)

        • 3.
          A conductor of length \( l \) is connected across an ideal cell of emf E. Keeping the cell connected, the length of the conductor is increased to \( 2l \) by gradually stretching it. If R and \( R' \) are initial and final values of resistance and \( v_d \) and \( v_d' \) are initial and final values of drift velocity, find the relation between:
          \( R' \) and \( R \)
          \( R' = 4R \)


            • 4.
              A small spherical shell \( S_1 \) has point charges \( q_1 = -3 \, \mu C \), \( q_2 = -2 \, \mu C \) and \( q_3 = 9 \, \mu C \) inside it. This shell is enclosed by another big spherical shell \( S_2 \). A point charge \( Q \) is placed in between the two surfaces \( S_1 \) and \( S_2 \). If the electric flux through the surface \( S_2 \) is four times the flux through surface \( S_1 \), find charge \( Q \).


                • 5.
                  A battery of emf \( E \) and internal resistance \( r \) is connected to a rheostat. When a current of 2A is drawn from the battery, the potential difference across the rheostat is 5V. The potential difference becomes 4V when a current of 4A is drawn from the battery. Calculate the value of \( E \) and \( r \).


                    • 6.
                      A current carrying circular loop of area A produces a magnetic field \( B \) at its centre. Show that the magnetic moment of the loop is \( \frac{2BA}{\mu_0} \sqrt{\frac{A}{\pi}} \).

                        CBSE CLASS XII Previous Year Papers

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