What is the electron volt (eV)?

The electron volt is a unit of energy like the joule (J).

However in quantum mechanics if the joule is used, then very small numbers would be obtained. These small numbers are very clumsy to use as a result a better unit to use is the electron volt.  

Fig 1

As you can see in fig 1, we have two metal plates that are connected to a power supply of e.m.f. 1 V. As a result a potential difference of 1 V will be set up be set up between the plates. An electric field will be set up between the plates as a result of the potential difference.

Now if a stationary electron is released from the negatively charged plate it will experience an acceleration due to the electric field and as a result will move towards the positively charged plate with increasing velocity.

When it would reached the positively charged plate it would have a certain velocity.

The Kinetic energy gained by the electron can be calculated by the following equation:

Kinetic energy gained E_k = Charge on particle * Potential difference between plates.

E_k = Q * V

Hence it can be deduce that if the charge is an electron then the kinetic energy that is gained by the electron is

Kinetic energy gained E_k = Charge on electron (elementary charge) * 1 V

   = 1 eV

Hence the eV is the energy that is gained by an electron or any particle of charge -e or +e when accelerated by a potential difference of 1 V 

If you want to know how many joule there is in 1 eV then it is as shown below

Kinetic energy gained E_k = Charge on electron (elementary charge) * 1 V

= 1.6 x 10^-19* 1

= 1.6 x10^-19 J

We can thus say that 1 eV is equivalent to 1.6 x 10 ^–19 J

As we have said above in quantum mechanics it is better to use the the eV because if the joule is used we would be dealing with small numbers which would make the works and calculations difficult.

Force, work, power and energy

Newton’s first law of motion

Newton’s second law of motion 

Weight of an object

Work done

Kinetic energy

Gravitational Potential energy

Gravitational potential energy to kinetic energy and vice versa

Power

Gravitational potential energy to kinetic energy and vice versa.

 

As we have seen in earlier post an object can have either gravitational potential energy or kinetic energy. However it is always possible for the object to have both kinetic energy and gravitational potential energy. Think of a plane flying at a certain height above the ground.

It is going to have kinetic energy due to its speed and gravitational potential energy due to its height.

Now what happens to a body that is either falling toward the ground or rising to a certain height. 

As you can see in fig 1 the object is rising and as a result its height is also rising, hence its potential energy is also increasing. Its kinetic energy is however decreasing. (see Principle of conservation of energy).

However the object in fig 2 is falling towards the ground. Since its height is decreasing, its gravitational potential energy must also be decreasing and its kinetic energy increasing.

Example 1

In this example a ball is released from rest from a height h.

If the ball is initially at rest then

v = 0  ms^-1 hence E_k = 0 J

However since the object is at a height h the E_p = mgh

When the ball is released it fall under the effect of the force of gravity, as a result it will accelerate downward and as a result the velocity of the object will increase  while the height of the object decreases.

Hence as the velocity decreases the kinetic energy decreases while the gravitational potential energy decreases as the height decreases.

However at all time    E_k +  E_p = Total energy and total energy is constant.

As the object reaches the ground the height becomes zero so does the gravitational potential energy while the kinetic energy reaches its maximum value. At this point all the gravitational potential energy would have been converted to kinetic energy.

When it reaches the ground h = 0 m hence E_p = 0 J

While E_k = 0.5 mv²

Example 1

A man of mass 64 kg jumps from a bridge 25 m high into a river.

(a) Calculate the gravitational potential energy of the man when he is on the bridge.

(b) What is his speed of entry into the water.

Now the man is on the bridge at a height of 25 m. It means that he has gravitational potential energy.

(a)  Gravitational potential energy E_p = mgh

                                                                = 64*9.81*25

                                                                = 15696J

                                                                 = 1.5 *10⁴J                                        

(b) When the person jumps the gravitational potential energy decreases as his height decreases. However as the person fall to the ground his speed increases and as a result the kinetic energy is completely converted to kinetic energy.

Hence what he reaches the river all the gravitational potential energy has been converted to kinetic energy.

Kinetic energy at surface of river =  1.5 *10⁴J

E_k = 0.5 mv²

1.5 *10⁴= 0.5 *64*v²

v = (1.5 *10⁴/0.5/64)^0.5

    = 21.65 m s^-1

=22 m s^-1

It is now time for a question. I will give you an answer to do. I will give the answer when some of you have given the answers.

Good luck.

A girl of mass 50 kg is trying to jump over a bar. She ran at a speed of and leaves the ground and successfully jumped over the bar.

(a) Calculate the kinetic energy that she has when she is running.

(b) Deduce the gravitational potential energy of the girl when she is at her maximum height.

(c) Calculate the height of the bar.

What is power?

Power is the rate of doing work.

From the definition we can deduce the following equation

Power = Work done /Time taken

The unit of power is the Watt (symbol W) or the Joule/second (J/s)

Example 1

A boy pushes a box and as a result does 120 J of work in 10 s. What is the power developed by the boy?

Power = Work done / time taken

= 120 /10

= 12 W or J/s

There is another definition for power that is often used. It is

Power is the rate of dissipation of energy or the rate of change of energy conversion.

Power = Energy dissipated / Time taken

Example 2

A girl climbs a staircase gaining 500 J of gravitational potential energy in 10 s.

What is the power developed by the girl?

Power = Energy conversion / Time taken

= 500 / 10

= 50 W or J/s

Example 3

During the boiling of some water 4000 J of heat energy is dissipated in the kettle’s heater in a time of 8 s. What is the power of the heater?

Power = Energy dissipated/Time taken

= 4000/8

= 500 W or J/s

It is now time to do some questions. It will give these questions after a few of you have supplied your answers.

1. A trains of mass 50000 kg accelerated form rest and reaches a velocity of 50 ms^-1 in 60 s.

(a) Calculate the kinetic energy gained by the train.

(b) Calculate the power of the train engine.

2. A lamp is rated 80 W. If it is switched on for two hours, how much light energy is dissipated.