Nuclear Structure And Radioactivity.

Atomic mass unit ( unified atomic mass unit (u)):-

The the masses of atom, nuclei and fundamental particles such as electron ,proton and neutron are expressed in unified atomic mass unit (u).
One u is defined as 1/12th of the mass of 6C¹² atom. The masses of other atoms are determined by measuring the positions of the lines they produce in a mass spectrograph related to that of 6C¹² atom.
[6C¹² carbon atom is stable and 6C¹⁴ is Radioactive used for carbon dating]
1u = 1/12 *[mass of 1 6C¹² atom]
1u = 1.6605 ×10^(-27) kg
Following are the masses of the common particles and atom in terms of unified atomic mass unit (u):-

• Election(e⁻) = 0.0005486 u
• Proton = 1.007276u
• α-particle = 4.001506u
• He atom = 4.002603u

Nuclear Size:-

According to Rutherford the side of atomic nucleus is 10^(-15) m.
The volume of a nucleus is directly proportional to the number of nucleons in it which is its mass number (A).
Volume∝A
⁴⁄₃πR³ ∝ A
R³∝ A
R ∝ A⅓
R=R°A⅓
Where R° is an empirical constant whose value is experimentally found to be roughly 1.2 into 10^(-15) m.
R°=1.2×10^(-15) m
The mass number 'A' is different for different atoms. Nuclei of different atoms have different radii , it's SI unit is 'Fermi'(F).
1 Fermi(F) = 10^(-15) m
R=R°A⅓
R=1.2 × 10^(-15) × A⅓

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R=1.2A⅓ Fermi

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Energy energy equivalent to '1u':-

According to Einstein the energy equivalent of mass ∆M is given by
∆E = [∆m]c²
where , ∆m = 1u
                     =1.6605×10(-27)Kg
                c = 2.9979×10^(8) m/s
Then according to the above result
∆E=1.4924×10^(-10)J
∆E=931.5 MeV
[MeV= million electron volts].

Typed by -  Saransh Agarwal (Tech N Moe)