Notes : Einstein's Mass Energy Equivalence Equation - Param Himalaya

Learn Einstein's Mass Energy Equivalence Equation (E=mc²), its derivation , class 12 physics , chapter 13 nuclei Param Himalaya 

Einstein's Mass Energy Equivalence Equation 

Using Einstein's mass–energy equivalence relation:

$E_T=mc^2$

where:

$E_T$ = Total energy of the particle

$m_0$ = Relativistic mass

c = Speed of light in vacuum

The total energy consists of rest-mass energy and kinetic energy:

$E_T = m_0c^2 + K.E.$

Therefore,

$mc^2 = m_0c^2 + K.E.$

From this,

$K.E. = mc^2 - m_0c^2$

$K.E. = (m-m_0)c^2$

Let,

$\Delta m = m-m_0$

Hence,

$K.E.=\Delta m\,c^2$

Result:

Kinetic energy of a particle = Change in mass × (speed of light)

Einstein's mass–energy equivalence relation is verified by nuclear reactions.

Numerical Example

Calculate the energy equivalent to 1 mg in eV.

Given:

$m = 1\,\text{mg} = 10^{-6}\,\text{kg}$

$c = 3 \times 10^8 \,\text{m s}^{-1}$

Using

$E = mc^2$

$E = 10^{-6}\times (3\times10^8)^2$

$E = 10^{-6}\times 9\times10^{16}$

$E = 9\times10^{10}\ \text{J}$

Since,

$1\,\text{eV} = 1.6\times10^{-19}\,\text{J}$

$E = \frac{9\times10^{10}}{1.6\times10^{-19}}$

$E = 5.625\times10^{29}\ \text{eV}$

Answer:

$\boxed{E = 5.625\times10^{29}\ \text{eV}}$

FAQ: Einstein's Mass Energy Equivalence Equation

Q1. What is Einstein's Mass-Energy Equivalence Equation?

Answer: Einstein's Mass-Energy Equivalence Equation states that mass and energy are interchangeable and related by the equation , where � is energy, � is mass, and � is the speed of light in vacuum.

Q2. What does mean $E=mc^{2}$?

Answer: The equation means that even a small amount of mass can be converted into a large amount of energy because the speed of light squared ($3 \times 10^{8}$) is an extremely large number.

Q3. Who proposed the Mass-Energy Equivalence Equation?

Answer: The equation was proposed by Albert Einstein in 1905 as part of his Special Theory of Relativity.

Q4. What do the symbols in $E=mc^{2}$ represent?

Answer:

E = Energy

m = Mass

C = Speed of light in vacuum ($3 \times 10^{8}$)

Q5. Why is the speed of light squared in the equation?

Answer: The speed of light squared acts as a conversion factor between mass and energy, showing that a tiny amount of mass corresponds to a very large amount of energy.

Q6. What are the applications of Mass-Energy Equivalence?

Answer: The equation is used in:

Nuclear power plants

Nuclear fusion and fission reactions

Particle physics

Understanding stellar energy production in stars

Q7. How is mass converted into energy in nuclear reactions?

Answer: During nuclear reactions, a small amount of mass is lost (mass defect). This lost mass is converted into energy according to $E=mc^{2}$.