Nuclear Stability and Nuclear Binding Energy

Nuclear Stability

Nuclear stability means nucleus is stable . Or it does not spontaneously emit any kind of radiation . On the other side, if the nucleus is not stable or unstable, it has the maximum probability of emitting some kind of radioactive particle, i.e., it is in the form radiation. So the radioactivity is associated with unstable nucleus:

Stable nucleus \(\rightarrow\) non-radioactive particles

unstable nucleus\(\rightarrow\) radioactive particles

Always remembered that less stable means more radioactive and also remembered it more stable means less radioactive.

We want to know why less stable is more radioactivity. What nature helps to nucleus get stable one? There are no abject theories to explain this nature, but we have one special idea to prove it, that is only general observations based on the available stable isotopes. It is shown that neutron to proton (n/p) ratio is the main factor in nuclear stability. This ratio will close to 1 for atoms of elements with low atomic number and increases as the atomic number increases. we have one simplest ways of predicting the nuclear stability .Which is based on whether nucleus contains an odd/even number of protons and neutrons as shown below.

• Nuclides which contain odd numbers of both protons and neutrons are the least stable means they are more radioactive.
• Nuclides which contain even numbers of both protons and neutrons are most stable means they are less radioactive.
• Nuclides which contain odd numbers of protons and even numbers of neutrons are less stable than nuclides containing even numbers of protons and odd numbers of neutrons.

Generally , nuclear stability related with the proton number and neutron number are odd or even .Nuclear stability is greater if the proton or neutron are even .

Some example

Based on the even-odd rule identify which one would you expect to be radioactive in each pair?

$$(a)\; _8^{16}O and _8^{17}$$

$$(b) \;\; _{17}^{35}Cl and \;\;_{17}^{36}Cl$$

$$(c) \;\; _{10}^{20}Ne and \;\;_{10}^{17}Ne$$

$$(d) \;\; _{20}^{40}Ca and \;\;_{20}^{45}Cl$$

$$(e) \;\; _{80}^{195}Hg and \;\;_{80}^{196}Cl$$

Answer

(a)Here The \(_8^{16}O\) have 8 protons and 8 neutrons both are even-even and the \(_8^{16}O\) have 8 protons and 9 neutrons one even and another odd . Therefore, \(_8^{17}O\) is more radioactive.

(b) The \(_{17}^{35}Cl\) has 17 protons and 18 neutrons one odd and another is even and the \(_{17}^{36}Cl\) has 17 protons and 19 neutrons both are odd . Hence, \(_{17}^{36}Cl\) is more radioactive.

(c) The \(_{10}^{20}Ne\) contains 10 protons and 10 neutrons ,where both are even and \(_{10}^{17}Ne\) contains 10 protons and 7 neutrons one even and another is odd. Therefore, \(_{10}^{17}Ne\) is more radioactive.

(d) The \(_{20}^{40}Ca\) has both even but \(_{20}^{45}Ca\) has one even and another odd . Thus, \(_{20}^{45}Ca\) is more radioactive.

(e) The \(_{80}^{195}Hg\) has the even number of protons and an odd number of neutrons and the \(_{80}^{196}Hg\) has the even number of protons and even number of neutrons. Therefore, \(_{80}^{195}Hg\) is radioactive.

Nuclear Binding Energy

The nuclear binding energy is defined as that energy which is required to break up a nucleus into its two components one is protons and another is neutrons. In fact, it is a quantitative measure of the nuclear stability. This nuclear binding energy concept is based on Einstein’s famous equation, \(E = mc^2\) ,

Here E is the energy m is mass and c is the velocity of light.

And according to this concept, the energy and mass can be convert each other ,that means energy can be converted into mass and mass can be converted into energy. Nucleus has generally two particles – protons and neutrons- in addition to other many elementary particles. Thus, we can say that the mass of the nucleus simply comes from the masses of protons and mass of neutrons. But it is not true ,the experiments have shown that the sum of the masses of protons and mass of neutrons is always greater than experimentally determined nuclear mass. Why does this ? The answer to this question is the way of nature of creates nucleus. When nature creates the nucleus, it will have protons and neutrons are bound together and puts them in a tiny space called nucleus. In order to bind protons and neutrons together but some energy is needed, which is taken from the masses of protons and mass of neutrons. It means our nature is very smart, it does not spend any o own energy but it converts some of the masses of protons and mass of neutrons into an energy and utilizes that energy to 2 binds the protons and neutrons in the nucleus. If we know how much mass is utilized,which is called mass defect we can convert easily it into binding energy using the Einstein’s equation.