Dual Nature of Light

  • Light is the transfer of energy.
  • The wave properties of light include frequency and wavelength. Frequency is inversely related to the wavelength by the speed of light. c =  where  = wavelength,  = frequency, and c = speed of light = 3 x 108 m/s
  • Light also has properties of particles. These particles have mass and velocity. A particle of light is called a photon.
  • How much energy is emitted by a photon of light can be calculated by E = h where E = energy of the photon, h = Planck’s constant = 6.626 x 10-34 J s, and  = frequency
  • To relate the properties of waves and particles, use DeBroglie’s equation: Where  = wavelength, h = Planck’s constant, m = mass and v = velocity.
  • Units:

 = waves per second (s-1)

 = nanometers, (nm) (note: 1 m = 1 x 109 nm),

E = Joules (J),

h, Planck’s constant = Joules x Seconds, (J s)

m = grams

v = meters per second, m/s

Practice Problems

  1. The threshold photoelectric effect in tungsten is produced by light of wavelength 260 nm. Give the energy of a photon of this light in joules.
  2. A mercury lamp emits radiation with a wavelength of 4.36 x 10-7 m. What is the frequency of the light?
  3. The brilliant read colors seen in fireworks are due to the emission of light with wavelengths around 659 nm. Calculate the frequency of red light of this wavelength.
  4. The blue color fireworks are produced when a compound emits light with a wavelength of 450 nm. What is the energy of the light emitted?
  5. Compare the wavelength for an electron (mass=9.11 x 10-31kg) traveling at a speed of 1.0 x 107 m/s with that for a ball (mass=0.10 kg) traveling at 35 m/s.
  6. It takes 7.21 x 10-19J of energy to remove an electron from an iron atom. What is the maximum wavelength of light that can do this?
  7. Calculate the de Broglie wavelength for each of the following:
  8. A proton with a velocity 90% of the speed of light. The mass of a proton is 1.66 x 10-27 kg.
  9. A 150 g ball with a velocity of 10 m/s.
  10. What is meant by the frequency of the wavelength? Describe the relationship between wavelength and frequency.
  11. What does it mean for something to have wavelike properties? Particulate properties?
  12. What is meant by an orbital?
  13. What happens when a hydrogen atom absorbs a quantum of energy?
  14. Define each of the following: photon, quantum number, ground state and excited state.

Dual Nature of Light

Practice Problems

  1. List all three equations used for the dual nature of light problems. List every variable and tell what it stands for and the units it needs to be in for each equation.
  2. What is meant by the frequency of the wavelength? Describe the relationship between wavelength and frequency.
  3. What does it mean for something to have wavelike properties? Particulate properties?
  4. The threshold photoelectric effect in tungsten is produced by light of wavelength 260 nm. Give the energy of a photon of this light in joules.
  5. A mercury lamp emits radiation with a wavelength of 4.36 x 10-7 m. What is the frequency of the light?
  6. The brilliant read colors seen in fireworks are due to the emission of light with wavelengths around 659 nm. Calculate the frequency of red light of this wavelength.
  7. The blue color fireworks are produced when a compound emits light with a wavelength of 450 nm. What is the energy of the light emitted?
  8. Compare the wavelength for an electron (mass=9.11 x 10-31kg) traveling at a speed of 1.0 x 107 m/s with that for a ball (mass=0.10 kg) traveling at 35 m/s.
  9. It takes 7.21 x 10-19J of energy to remove an electron from an iron atom. What is the maximum wavelength of light that can do this?
  10. Calculate the de Broglie wavelength for each of the following:
  11. A proton with a velocity 90% of the speed of light. The mass of a proton is 1.66 x 10-27 kg.
  12. A 150 g ball with a velocity of 10 m/s.
  13. What happens when a hydrogen atom absorbs a quantum of energy?
  14. Define each of the following: photon, quantum number, ground state and excited state.
  15. What is meant by an orbital?
  16. How does the quantum mechanical model of the atom differ from Bohr’s planetary model of the atom?
  17. What causes an atom to emit different colors of light?