5.5.2 Electromagnetic radiation from stars

When electrons are bound to their atoms in a gas they can only exist in one of a discrete set of energies - the energy levels of an electron:

• An electron cannot have a quantity of energy between two levels
• The energy levels are negative because external energy is required to remove an electron from the atom.
• The energy leve with the most negative value is the ground state/ground level
• An electron with zero energy is free from the atom

An atom is said to be excited when an electron moves from a lower to a higher energy level within an atom in a gas. Raising an electron into a higher energy level requires external energy - for example when photons of specific energy are absorbed by the atom. Similarly, when an electron moves from a higher energy level to a lower energy level it loses energy. As we know, energy is conserved. This means that as the electron makes a transition between levels a photon is emitted from the atom (this can be known as de-excitation). In order for an electron to make a transition from -3eV to -6.8eV (for example) it must lose 3.8eV. It emits this in the form of a photon with energy 3.8eV. The energy of a photon emitted in an electron transition from a higher to lower energy level is given by the equation:

E = hf

NOTE: it is important to realise that each element has its own unique set of energy levels.

Different atoms have different spectral lines - the spectra from starlight can be used to identify the elements within stars without a direct sample (as a ample of a star is pretty hard to obtain lol). There are three kinds of spectra:

• Emission line spectra - each element produces a unique emission line spectrum because of its unique set of energies
• Continuous spectra - all visible frequencies/wavelengths are present. The atoms of a heated solid metal (e.g. a filament lamp) will produce this type of spectrum
• Absorption line spectra - this type of spectrum has a series of dark spectral lines against a continuous spectrum. The dark lines have the same wavelengths as the bright emission spectral lines for the same gas atoms.

If the atoms are excited then when the electrons drop back into the lower energy levels they emit photons with a set of discrete frequencies specific to the element. This produces a characteristic emission line spectrum and each spectral line corresponds to photons with a specific wavelength. These spectra can be observed in a laboratory from heated gases. Each coloured line represents a unique wavelength/frequency of photon emitted when an electron moves between two specific energy levels.

A bit more on absorption line spectra: This is formed when light from a source that produces a continuous spectrum passes through a cooler gas. As the photons pass through the fas some are absorbed by the gas atoms, raising electrons up into higher energy levels and so exciting the atoms. Only photons with an energy exactly equal to the difference between the different energy levels are absorbed (meaning that only a specific wavelength are absorbed) - this creates dark lines in the spectrum. These lines show which photons have been absorbed. When the electron drops back down to a lower energy level the photons are re-emitted in all directions so the intensity in the original direction is reduced. 

We need to know about how we detect which elements are present on stars (without a sample). Basically, when the light from a star is analysed it is found to be an absorption line spectrum. Some wavelengths of light are missing - these are the photons that have been absorbed by atoms of cooler gas in the outer layer of the star. If we know the line spectrum of a particular element we can check whether the element is present in the star (if a particular element is present its characteristic pattern of spectral lines will appear as dark lines in the absorption line spectrum).

A diffraction grating is an optical component with regularly spaced slits/lines that diffract and split light into beams of different colours travelling in different directions. These beams can be analysed to determine the wavelengths of spectral lines in the laboratory/from starlight. It is slightly different to the double slit (Youngs Double Slit experiment) in which it consists of a large number of lines ruled on a glass/plastic slide and each line diffracts like a slit producing a clearer and brighter interference pattern than the double slit. The direction of the beams produced depends on the spacing of the lines/slits of the grating and the wavelength. 

Like in the double slit, maxima and minima are still formed. The interference pattern is the result of the superposition of the diffracted waves in the space beyond the grating.  The formation of maxima at a particular point depends on the path difference and the phase difference of the waves from all the slits.

The zero-order maxima (n=0) is formed when the path difference is zero, that is at an angle θ=0. The angle θ is measured relative to the normal to the grating/to the direction of incident light. For the nth order maxima the path difference QY at an angle θ will be equal to nλ. Also, the distance PQ is the separation between adjacent lines/slits on the grating. 

We can use the following equation to determine any of the above features:

sinθ = QY/QP = nλ/d

dsinθ = nλ

NOTE: n must be an integer value. 

Thus us known as the grating equation. It can be used to accurately determine the wavelength of monochromatic light.


At any given temperature (above absolute zero) an object emits electromagnetic radiation of different wavelengths and different intensities. We can model a hot object as a black body. This is an idealised object that absorbs all the electromagnetic radiation that shines onto it and (when in thermal equilibrium) emit a characteristic distribution of wavelengths at a specific temperature.

Wein's displacement law relates the absolute temperature (T) of a black body to the peak wavelength (λmax) at which intensity is a maximum. It's a bit confusing because λmax isn't the maximum λ, it's actually the most abundant λ. The law states that λmax is inversely proportional to T:

λmax ∝ 1/T

Therefore, for any black body emitter λmax T = constant. the constant is Wein's constant - 2.90x10^-3 mK.

Modelling objects as approximate black bodies helps scientists to determine temperatures of objects simply by analysing the electromagnetic radiation they emit. It is important to realise that, as the temperature of an object changes, the distribution of the emitted wavelengths changes. As temperature increases, the peak wavelength reduces and the peak of the intensity-wavelength graph becomes sharper.

Stephan's law: The total power radiated by a star is called luminosity. Stephan's law states that the total power radiated per unit surface area of a black body is directly proportional to the fourth power of the absolute temperature of the black body. Luminosity can be found using the equation below:

L = 4πr²σT⁴

NOTE: σ is known as the Stephan constant (5.67 x 10^-8 WmT^-2K^-4).

Stephan's law shows that the the luminosity (L) of a star is directly proportional to:

• it's radius² (L ∝ r²)
• it's surface area (L ∝ 4πr²)
• it's surface absolute temperature⁴ (L ∝ T⁴)

We can use both Wein's displacement law and Stephan's law to estimate the radius of a distant star. Once the radius is known we can calculate it's density and mass using Newton's law of gravitation.