# AQA A Level Physics复习笔记2.5.2 Energy Levels & Photon Emission

### Line Spectra & Energy Levels

#### Atomic Energy Levels

• Electrons in an atom can have only certain specific energies
• These energies are called electron energy levels

• They can be represented as a series of stacked horizontal lines increasing in energy
• Normally, electrons occupy the lowest energy level available, this is known as the ground state
• Electrons can gain energy and move up the energy levels if it absorbs energy either by:
• Collisions with other atoms or electrons
• Absorbing a photon
• A physical source, such as heat

• This is known as excitation, and when electrons move up an energy level, they are said to be in an excited state
• If the electron gains enough energy to be removed from the atom entirely, this is known as ionisation
• When an electron returns to a lower energy state from a higher excited state, it releases energy in the form of a photon

Electron energy levels in atomic hydrogen. Photons are emitted when an electron moves from a higher energy state to a lower energy state

#### Line Spectra

• Line spectra is a phenomenon which occurs when excited atoms emit light of certain wavelengths which correspond to different colours
• The emitted light can be observed as a series of coloured lines with dark spaces in between
• These series of coloured lines are called line or atomic spectra

• Each element produces a unique set of spectral lines
• No two elements emit the same set of spectral lines, therefore, elements can be identified by their line spectrum
• There are two types of line spectra: emission spectra and absorption spectra

#### Emission Spectra

• When an electron transitions from a higher energy level to a lower energy level, this results in the emission of a photon
• Each transition corresponds to a different wavelength of light and this corresponds to a line in the spectrum
• The resulting emission spectrum contains a set of discrete wavelengths, represented by coloured lines on a black background
• Each emitted photon has a wavelength which is associated with a discrete change in energy, according to the equation:

• Where:
• ΔE = change in energy level (J)
• h = Planck’s constant (J s)
• f = frequency of photon (Hz)
• c = the speed of light (m s-1)
• λ = wavelength of the photon (m)

• Therefore, this is evidence to show that electrons in atoms can only transition between discrete energy levels

Emission spectrum of Hydrogen gas

#### Absorption Spectra

• An atom can be raised to an excited state by the absorption of a photon
• When white light passes through a cool, low pressure gas it is found that light of certain wavelengths are missing
• This type of spectrum is called an absorption spectrum

• An absorption spectrum consists of a continuous spectrum containing all the colours with dark lines at certain wavelengths
• These dark lines correspond exactly to the differences in energy levels in an atom
• When these electrons return to lower levels, the photons are emitted in all directions, rather than in the original direction of the white light
• Therefore, some wavelengths appear to be missing

• The wavelengths missing from an absorption spectrum are the same as their corresponding emission spectra of the same element

Absorption spectrum of Hydrogen gas

### 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

#### Worked Example

Some electron energy levels in atomic hydrogen are shown below.The longest wavelength produced as a result of electron transitions between two of the energy levels is 4.0 × 10–6 m.a) Draw and mark:

• The transition giving rise to the wavelength of 4.0 × 10–6 m with letter L.
• The transition giving rise to the shortest wavelength with letter S.

b) Calculate the wavelength for the transition giving rise to the shortest wavelength.

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)