Test: Atomic Nucleus

The nuclide (nucleus) consists of neutrons and protons (when combined called nucleons).
Thus,
No. of protons in 92U²³⁸ = 92,
No. of neutrons = 146 (238 – 92)
No. of nucleons = 238 (146 + 92)

Most nuclei are approximately spherical. The average radius of a nucleus with A nucleons is R = R₀A^1/3, where R⁰ = 1.2*10^-15 m. The volume of the nucleus is directly proportional to the total number of nucleons. This suggests that all nuclei have nearly the same density.

R∝A^1/3
A(mass no.)=n+p
R/x=(10/80)^1/3
R/x=(1³/2³)^1/3
R/x=1/2
X=2R

Binding energy per nucleon is the ratio of the binding energy of a nucleus to the number of the nucleons.

Binding energy per nucleon = (Total binding energy) / (Number of nucleon)

Measure of stability of the nucleus: Larger the binding energy per nucleon, the greater the work that must be done to remove the nucleon from the nucleus, the more stable the nucleus.

The atomic number or proton number (symbol Z) of a chemical element is the number of protons found in the nucleus of every atom of that element. The atomic number uniquely identifies a chemical element. It is identical to the charge number of the nucleus

We use the concept of conservation of energy and distance of closest approach in Rutherford's alpha scattering experiment to find the radius of the nucleus is proportional to the Mass Number. The consequence of this is that the density of the nucleus is a constant, independent of mass number for all nuclei.
 

For A nucleons
R=R_o​A^1/3 [R_o=constant]
 So, R∝A^1/3

The ratio of the volume of the atom and the volume of the nucleus is 10¹⁵
The radius of an atomic nucleus is of the order of 10⁻¹³cm or 10⁻¹⁵m or one Fermi unit.
On the other hand, the radius of an atom is of the order of 10⁻⁸cm or 10⁻¹⁰m or one angstrom unit.
Note:
The radius of the nucleus is much smaller than atomic radius.
The ratio of atomic radius to radius of nucleus is 10⁻¹⁰m /10⁻¹⁵m ​=10⁵
Volume is proportional to cube of radius.
The ratio of atomic radius to radius of nucleus is (10⁵)³=10¹⁵

Excluding the lighter nuclei, the average binding energy per nucleon is about 8 MeV. The maximum binding energy per nucleon occurs at around mass number A = 50, and corresponds to the most stable nuclei.

No of neutrons are given by: (A−Z)
Given an atomic number (Z) and mass number (A), you can find the number of protons, neutrons, and electrons in a neutral atom. For example, a lithium atom (Z=3,A=7 amu) contains three protons (found from Z), three electrons (as the number of protons is equal to the number of electrons in an atom), and four neutrons (7–3=4).