Size of Nucleus

 

Size of Nucleus

As a measure of size of nucleus Geiger and Marsden(on Rutherford’s suggestion) performed α-particles scattering experiment on thin gold foils to find the distance of closest approach of the α-particles to the nucleus. They used α-particle of kinetic energy about 5.5 MeV and using principle of the conservation of energy they found the distance of closest approach about 4.0×10^–14 m.

But we cannot say that the alpha particle exactly touches the nucleus, if we use more energetic α-particles, we might get more closer to the nucleus.

More scattering experiments were performed in which fast moving electrons were used instead of α-particles and the sizes of nuclei of various elements have been accurately measured.

It has been found that radius of nucleus R is directly proportional to one third power of mass number A of the nucleus.

i.e.,      R ∝ A^1/3

Or       R = R₀A^1/3

where R₀ = 1.2×10^–15 m.

Nuclear Volume

(Size of Nucleus)

Volume of a nucleus of radius R is given by

As R = R₀A^1/3

So,

Or

V ∝ A

Therefore volume of the nucleus is directly proportional to the mass number A, i.e., the number of nucleons present in the nucleus.

 

Nuclear Density

(Size of Nucleus)

Nuclear density is the ratio of mass of the nucleus and its volume.

If m the average mass of a nucleon of an element of mass number A, then

total mass of the nucleus = mA

And volume of the nucleus is given by

So,

density of the nucleus(ρ) = mass of nucleus/volume of nucleus

here m and R₀ are constant therefore density of nucleus is same for all elements.

As m = 1.66×10^-27 Kg and R₀ = 1.2×10^–15 m

We get,

density of the nucleus (ρ) = 2.29×10¹⁷ Kg/m³

 

 

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