The alpha particle scattering experiment and many other measurements using different methods have been carried out on the nuclei of various atoms.

**Size and
density of the nucleus**

The alpha particle scattering experiment and many other measurements
using different methods have been carried out on the nuclei of various atoms.
The nuclei are found to be approximately spherical in shape. It is experimentally
found that radius of nuclei for *Z *>
10, satisfies the following empirical formula

Here *A *is the mass
number of the nucleus and the constant R_{0} = 1.2 F, where 1 F = 1 Ã—
10^{â€“15} m. The unit fermi (F) is named after Enrico Fermi.

** **

**EXAMPLE 8.7**

Calculate the radius of ^{197}_{79}*Au *nucleus.

**Solution**

According to the equation (8.19),

*R *= 1.2 Ã— 10^{-15} Ã— (197)^{1/3}
= 6.97 Ã— 10^{-15}*m*

Or *R = *6.97 F

**EXAMPLE 8.8**

Calculate the density of the nucleus with mass number *A*.

**Solution**

From equation (8.19), the radius of the nuclei satisfy the equation
= *R*_{0}*A ^{1/}*

*V *= 4/3 Ï€*R*^{3} =
4/3 Ï€*R*^{3}*A*

By ignoring the mass difference between the proton and neutron,
the total mass of the nucleus having mass number *A *is equal to *A.m *where *m *is mass of the proton and is equal to
1.6726 x 10^{-27} kg.

The above expression shows that the nuclear density is
independent of the mass number *A*. In
other words, all the nuclei (*Z *>
10) have the same density and it is an important characteristics of the nuclei.

We can calculate the numerical value of this density by
substituting the corresponding values.

It implies that nucleons are extremely tightly packed in the
nucleus and compare this density with the density of water which is 103 kg m^{-3}.

A single teaspoon of nuclear matter would weigh about trillion
tons.

Tags : Nuclear Physics , 12th Physics : UNIT 9 : Atomic and Nuclear Physics

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12th Physics : UNIT 9 : Atomic and Nuclear Physics : Size and density of the nucleus | Nuclear Physics

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