NUCLEI part 01

                 NUCLEI

Atomic No. 

Defined by the No. Of protons present in nucleus and also the no. Of electrons present in the atom denoted by Z. 

Mass No. 

It is defined by the sun of proton and Neutron present in the nucleus of an atom denoted by A. 

Nucleons

The protons and neutrons in the nucleus are collectively known as nucleons. 

Representation of an element's atom 

X = element

Z = atomic no. 

A = mass no. 

Neutrons

It is defined by the difference of mass no. And atomic no. 

No. Of neutrons = A - Z

Isotopes

Atoms having same atomic no. But different mass no. 

Ex - 

Isobars

Atoms having same mass no. But different atomic no. 

Ex - 

Isotones

Atoms having equal no. Of neutrons but different atomic no. 

Ex - 

Atomic mass unit

One atomic mass unit is defined as 1/12th of the actual mass of carbon 12 atom. It is denoted by any or just by u. 

1 a m u  = 1.66 × 10(of power of -27) kg

Electron volt

It is defined as the energy acquired by an electron when it is accelerated through a potential difference of 1 volt and is denoted by eV. 

1eV = 1.602 × 10(of power of -19) J

1MeV = 1.602 × 10( of power of -13) J

Relation between amu and MeV

1 amu = 931MeV

Size of a Nucleus

From experiment, it is found that volume of nucleus is proportional to mass no. 

           

If R be the radius of nucleus

Then, (4/3)×π×R×R×R is directly proportional to A

R×R×R  is directly proportional to A

R is directly proportional to A(of power of 1/3) 

R = Ro×A(of power of 1/3) 

Where, Ro = 1.2fm

               Ro = 1.2 × 10(of power of -15) 

Mass defect

It is found that the mass of stable nucleus or mass of nucleus at rest is always less than the total mass of constituent protons and neutrons, denoted by (del.m) 

If mN, mp and mn are rest mass of nucleus, protons and neutrons and if Z be the no. Of protons, (A-Z) is the no. Of neutrons

Mass defect (del.m) = Zmp + (A-Z) mn - mN

Packing fraction Ratio

It is defined by the ratio of mass defect to mass no. For an atom

Packing fraction = (del.m)/A

P.F = [Zmp + (A-Z) mn - mN]/A

Binding Energy

Defined by the maximum energy required to separate the constituent particles present in nucleus, denoted by B

B = (del.m) × c×c

Binding energy  per nucleon

Defined by the ratio of binding energy to the mass no. 

Binding energy per Nucleon = B/A

B. E. P. N = (del.m) × c×c/A

B. E. P. N = [z×mp + (A-Z) mn - mN] c×c/A

Binding energy curve and it's outcomes 

1. Binding energy per nucleon is very low for light nuclei such as 

2. B. E. P. N  rises rapidly with increase in volume of A upto A = 20

3. B. E. P. N  increases gradually from mass no. A = 20 to A = 40

4. The curve is almost flat between mass no. 40 and 120. This means that the variation in B. E. P. N from this range is very small. 

The value of B. E. P. N for this range is about 8.5 million electron volt and it is maximum for iron  of about 8.8 meV. 

5. The B. E. P. N decreases slowly and continuously from mass no. 120 to 240 . It reaches a value of 7.6MeV at A = 238.

6. B. E. P. N  is smaller for light and heavier nuclei, therefore, light and heavier nuclei are less stable than middle one. 

7. In order to attain high value of B. E. P. N the heavier nuclei may split into lighter nuclei process of fission and the lighter nuclei may unite to form heavier nuclei process of fusion.