Difference in discrete energy levels

• The difference between two energy levels is equal to a specific photon energy
• The energy (hf) of the photon is given by:

ΔE?=?hf?=?E₂?-?E₁

• Where:
  • E₁?= Energy of the higher level (J)
  • E₂?= Energy of the lower level (J)
  • h?=?Planck's constant?(J s)
  • f?= Frequency of photon (Hz)

• Using?the wave equation, the wavelength of the emitted, or absorbed, radiation can be related to the energy difference by the equation:

• This equation shows that the larger the difference in energy of two levels ΔE?(E₂?- E₁) the shorter the wavelength?λ?and vice versa

Part (a)

• Photon energy and wavelength are inversely proportional
• Therefore, the largest energy change corresponds to the shortest wavelength (line S)
• The smallest energy change corresponds to the longest wavelength (line L)

Part (b)

• • Consider the different ways that the electron may become less excited and emit photons

Step 1: Consider first the case where the electron goes directly from the fourth energy level (n = 4) to the ground state (n = 1)

• • This is the first way that the electron may move between these energy levels
  • Therefore, this is the highest energy photon that could be emitted since it has the highest energy change
  • Each arrow downwards represents a different wavelength of photon released

  

Step 2: Consider the cases where two energy level changes are used

• • The first is from the fourth energy level (n = 4) to the third energy level (n = 3) and then on to the ground state (n = 1)
  • The second is from the fourth energy level (n = 4) to the second energy level (n = 2) and then on to the ground state (n = 1)
  • These pathways produce four different photons of different wavelengths and energy

Step 3: Consider the case where all possible energy level changes are used

• • In this final case, the electron could move down through every energy level, the fourth level to third, then second and ground state. (n = 4 to 3 to 2 to 1).
  • While the energies of the photons from n = 4 to 3 and n = 2 to 1 are already accounted for in the previous step, one new photon of a different wavelength is produced in the transition from n = 3 to 2.

Step 4: State the final answer

• • There are?six?possible wavelengths that come from the different energy level transitions