Nuclei

Notes

1. Nucleus

Nucleus: A positive region with a positive particle is called the nucleus.

Nucleon: The particles which are present in the nucleus of an atom are called nucleons.

The nucleons are:

• Proton
• Neutron

The mass of the nucleus is due to the mass of nucleons.

2. Atomic Number

Atomic Number: The number of protons and electrons is called the atomic number.

Z = P = e

3. Atomic Mass Number

Atomic Mass Number: Number of protons + number of neutrons.

A = P + N

4. Atomic Mass

Atomic Mass: The summation of the masses of protons and neutrons is called atomic mass.

Atomic mass = Atomic mass number

The mass of an atom is measured in a unit called atomic mass unit (a.m.u.).

1 a.m.u. = 1 u

It is defined as one-twelfth of the mass of one atom of carbon-12.

1 a.m.u. = (1/12) × mass of one atom of C-12

Since:

Mass of 6.023 × 10²³ atoms of carbon = 12 g

Therefore:

Mass of one atom of carbon = 12/(6.023 × 10²³) g

Hence:

1 a.m.u. = (1/12) × [12/(6.023 × 10²³)] g

1 a.m.u. = 1.66 × 10⁻²⁴ g

1 a.m.u. = 1.66 × 10⁻²⁷ kg

Mass of Proton, Electron and Neutron

m_p = 1.00727 u = 1.6722 × 10⁻²⁷ kg

m_e = 0.00055 u = 9.1 × 10⁻³¹ kg

m_n = 1.00866 u = 1.6745 × 10⁻²⁷ kg

5. Isotopes

Isotopes: Same atomic number but different mass number.

Examples:

¹⁶₈O, ¹⁷₈O, ¹⁸₈O

³⁵₁₇Cl, ³⁷₁₇Cl

¹⁹₉F

³⁹₁₉K, ⁴⁰₁₉K, etc.

6. Isobars

Isobars: Same mass number but different atomic number.

Examples:

⁴⁰₁₈Ar, ⁴⁰₂₀Ca

³₁H, ³₂He

⁷₃Li, ⁷₄Be, etc.

7. Isotones

Isotones: Same number of neutrons.

Examples:

⁴⁰₁₈Ar and ⁴⁰₁₉K

¹⁴₆C and ¹⁴₇N

¹⁹₉F and ²⁰₁₀Ne

²⁴₁₁Na and ²⁴₁₂Mg, etc.

8. Size of the Nucleus

The volume of the nucleus is proportional to the mass number.

V ∝ A

But:

V = (4/3)πR³

Due to the spherical shape of the nucleus:

(4/3)πR³ ∝ A

Therefore:

R³ = Constant × A

Hence:

R = (Constant)^1/3A^1/3

Since:

(Constant)^1/3 = R₀ = 1.2 × 10⁻¹⁵ m

Therefore:

R = R₀A^1/3

Hence:

R ∝ A^1/3

9. Density of the Nucleus

Mass per unit volume is called density.

Density = Mass/Volume

Mass of nucleus:

Mass = (P + N) × 1 a.m.u.

Volume:

V = (4/3)πR³

Therefore:

ρ = [(P + N)1 a.m.u.]/[(4/3)πR³]

Since:

P + N = A

and

R = R₀A^1/3

Therefore:

ρ = A × 1 a.m.u./[(4/3)π(R₀A^1/3)³]

ρ = A × 1 a.m.u./[(4/3)πR₀³A]