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ASPhysicsAQARevision Notes2. Particles & Radiation2.4 The Photoelectric Effect2.4.1 The Electronvolt

The Electronvolt (AQA AS Physics)

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Katie M

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Katie M

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The Electronvolt

  • The electronvolt is a unit which is commonly used to express very small energies
  • This is because quantum energies tend to be much smaller than 1 Joule
  • The electronvolt is derived from the definition of potential difference:

V space equals fraction numerator space E over denominator Q end fraction

  • Where:
    • V = potential difference (V)
    • E = energy (J)
    • Q = charge (C)
  • When an electron travels through a potential difference, energy is transferred between two points in a circuit or electric field
  • If an electron, with a charge of 1.6 × 10-19 C, travels through a potential difference of 1 V, the energy transferred is equal to:

E space equals space Q V space equals space open parentheses 1.60 space cross times space 10 to the power of negative 19 end exponent close parentheses space straight C space cross times space 1 space straight V space equals space 1.60 space cross times space 10 to the power of negative 19 end exponent space straight J

  • Therefore, an electronvolt is defined as:

The energy gained by an electron travelling through a potential difference of one volt

1 space eV space equals space 1.60 space cross times space 10 to the power of negative 19 space end exponent straight J

  • To convert between eV and J:
    • eV → J: multiply by 1.6 × 10-19
    • J → eV: divide by 1.6 × 10-19

Relation to Kinetic Energy

  • When a charged particle is accelerated through a potential difference, it gains kinetic energy
  • If an electron accelerates from rest, an electronvolt is equal to the kinetic energy gained:

e V space equals space 1 half m v squared

  • Where:
    • e = charge of an electron (1.60 × 10–19 C) 
    • V = potential difference (V)
    • m = mass of the particle (kg)
    • v = velocity of the particle (m s–1)
  • Rearranging the equation gives the speed of the electron:

v space equals space square root of fraction numerator 2 e V over denominator m end fraction end root

Worked example

(a)
An electron has an energy of 2.4 eV.
Give the energy of the electron in joules.
 
(b)
A photon has an energy of 4.9 × 10−19 J.
Give the energy of the photon in electronvolts.
 

Answer:

Part (a)

E space equals space 2.4 space eV space equals space 2.4 space cross times space open parentheses 1.6 cross times 10 to the power of negative 19 end exponent close parentheses

E space equals space 3.8 cross times 10 to the power of negative 19 end exponent space straight J

Part (b)

E space equals space 4.9 cross times 10 to the power of negative 19 end exponent space straight J space equals space fraction numerator 4.9 cross times 10 to the power of negative 19 end exponent over denominator 1.6 cross times 10 to the power of negative 19 end exponent end fraction

E space equals space 3.1 space eV

Worked example

Show that the photon energy of light with wavelength 700nm is about 1.8 eV.

Answer:

Step 1: Write the equation for photon energy

E space equals fraction numerator space h c over denominator lambda end fraction

Step 2: Calculate the photon energy in Joules

E space equals fraction numerator space h c over denominator lambda end fraction space equals space fraction numerator open parentheses 6.63 space cross times space 10 to the power of negative 34 end exponent close parentheses space cross times space open parentheses 3.0 space cross times space 10 to the power of 8 close parentheses space over denominator 700 space cross times space 10 to the power of negative 9 end exponent end fraction space equals space 2.84 space cross times space 10 to the power of negative 19 end exponent space straight J

Step 3: Convert the photon energy into electronvolts

1 space eV space equals space 1.60 space cross times space 10 to the power of negative 19 end exponent space straight J

J → eV: divide by 1.60 × 10-19

E space equals space fraction numerator 2.84 space cross times space 10 to the power of negative 19 end exponent over denominator 1.60 space cross times space 10 to the power of negative 19 end exponent end fraction space equals space 1.78 space eV

Examiner Tip

Converting between electronvolts and joules is a skill that you will use a lot in exam questions on this topic. You do not need to remember the value of 1 eV as this will be given on your datasheet, but you do need to be confident in the conversion so that it doesn't slow you down.

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    Katie M

    Author: Katie M

    Expertise: Physics

    Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.