Class 9th

Physics

Chapter 06

Work And Energy (Mass-energy equivalence theory)

Mass-energy equivalence theory was proposed by Albert Einstein. This theory gives relationship between mass and energy in rest frame.

Statement:

Einstein Mass-energy equivalence theory states that ,

‘ Mass and energy are interconvertable . Mass can be converted to energy and energy can be converted to mass’.

Mathematical Form:

Mathematically, Einstein’s mass energy equation is given by ,

Energy= mass× the speed of light squared

E = energy (measured in joules)

m = mass of object

c = speed of light (measured in metres per second )

Speed of light has a constant value 3×10⁸ metre per second , this value needs to be squared. In simple words we can say that , Mass and energy are same physical entities and can be changed into one another.

For example:

The mass of a small marble is 20 gram. The energy it contains is equal to 1.8 × 10¹⁵ Joule which is equivalent to the energy produced by 500,000 Ton Hydrogen bomb. A question here arises that we are always afraid of Hydrogen bomb but not of a marble . Why?

Reason:

A 20 gram marble contains 1.8 × 10¹⁵ Joule energy. But it is almost impossible to convert this marble into energy. It is converted by matter – antimatter annihilation. When a subatomic particle of matter collides with it’s anti-matter it is converted to energy in the form of electromagnetic waves.

Example 6.4

What is the amount of energy released, when 50kg person is completely converted in to energy.

Given data :

mass of energy= m = 50kg

speed of light= c = 3×10⁸ m/s

Required:

Energy = E = ?

Solution:

We know that , from mass-energy equivalence theory

E = mc² ….. i

Putting values,

E = 50 kg × ( 3×10⁸ m/s)²

E = 50 kg × (9×10¹⁶)

E = 450 × 10¹⁶ Joule

E = 4.5 × 10² × 10¹⁶ Joule

E = 4.5 × 10¹⁸ Joule

So , the energy produced by only 50 kg of mass , is 4,500,000,000,000,000,000 Joule which is incredibly large amount of energy which is equal to billion tons of TNT.

Assignment 6.4

How much energy is generated when mass of 1 gram is completely converted into energy.

Given Data:

Mass = m = 1 g = (1/1000) kg = 0.001 kg

Speed of light= c = 3×10⁸ m/s

Required:

Energy= E = ?

Solution:

As we know that , Einstein’s mass energy equivalence theory is given by ,

Energy= mass × speed of light squared

E = mc² ……. i

E = 0.001 kg × (3× 10⁸ m/s)²

E = 1× 10^-3 × 9 × 10¹⁶ Joule

E = 9 × 10^-3+16Joule

E = 9× 10¹³ Joule

So , the energy generated from 1 g of mass is 9× 10¹³ Joule .

Related Example:

Find your mass and convert it into Energy.

Given Data :

Mass = m = 60 kg

Speed of light= c = 3×10⁸ m/s

Required:

Energy= E = ?

Solution:

As we know that , Einstein’s mass energy equivalence theory is given by ,

Energy= mass × speed of light squared

E = mc² ……. i

E = 60 kg × (3× 10⁸ m/s)²

E = 60 × 9 × 10¹⁶ Joule

E = 540 × 10¹⁶ Joule

E = 5.4 × 10² × 10¹⁶ Joule

E = 5.4 × 10¹⁸ Joule

So , the energy generated from 50 kg of mass is 5.4 × 10¹⁸ Joule .

Related Example 2:

How much mass can be converted to energy equal to 9×10¹⁶ Joule?

Given Data:

Energy= E = 9×10¹⁶ Joule

Speed of light= c = 3 × 10⁸ m/s

Required:

Mass of object= m = ?

Solution:

We know that , mass- energy equivalence theory is given by ,

Energy= mass × speed of light squared

E = mc² ….. i

For mass , rearranging the equation

m = E / c²

m = (9×10¹⁶ Joule ) / ( 3× 10⁸ m/s)²

m = ( 9× 10¹⁶ Joule / 9 × 10¹⁶ m²/s² )

m = 1 kg

So , the energy of 9×10¹⁶ Joule can be generated by 1kg of matter.

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