Nuclei

13.2 Atomic mass of ${}_{10}{}^{20}Ne$ neon isotope, $m_1$ = 19.99 u ad the abundance ${\eta }_1$ = 90.51 %

Atomic mass of ${}_{10}{}^{21}Ne$ neon isotope, $m_2$ = 20.99 u ad the abundance ${\eta }_2$ = 0.27 %

Atomic mass of ${}_{10}{}^{22}Ne$ neon isotope, $m_3$ = 21.99 u ad the abundance ${\eta }_3$ = 9.22 %

The average atomic mass of neon is given as:

m = $\frac{m_1{\eta }_1+m_{2{\eta }_2}+m_3{\eta }_3}{{\eta }_1+{\eta }_2+{\eta }_3}$ = $\frac{19.99*90.51+20.99*0.27+21.99*9.22}{90.51+0.27+9.22}$ = $\frac{2017.71}{100}$ = 20.1771 u

The principle of mass-energy equivalence, given by Einstein's equation:

$E = mc^2$It states that mass and energy are interchangeable.

A small amount of mass can be converted into a large amount of energy because the speed of light $(c = 3 \times 10^8 \, \text {m/s})$ is very large and appears squared in the equation.

Significance in Nuclear Reactions:

• Helps in calculating the energy release in Nuclear Reactions
• Provides explanation for powering Nuclear Reactors and the Sun
• Explanation of Binding Energy of Nucleous

Nuclear Binding Energy is the amount of energy required to completely dismantle a nucleus into its individual protons and neutrons which is equivalent to the amount of energy to form a nucleous from its constituent nucleons (protons and neutrons).

Binding energy is calculated using Einstein's mass-energy equivalence relation:

$B.E. = \Delta m \cdot c^2$Where:

• $\Delta m$ = mass defect (in kg or amu)

• $c$ = speed of light $(3 \times 10^8 \, \text {m/s})$ (3*108m/s)