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Astronomy Principles and Practice Fourth Edition.pdf

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Electromagnetic radiation 21<br />

If, for example, the wavelength of 1 m is involved, then its associated frequency is given by<br />

ν = c λ = 3 × 108<br />

1<br />

= 100 × 10 6 = 100 MHz.<br />

4.4.2 The photon nature of radiation<br />

There is another aspect to the description of electromagnetic radiation that is important in terms of the<br />

atomic processes occurring in astronomical sources <strong>and</strong> in the process of detection by observational<br />

equipment.<br />

At the turn of the twentieth century, it was demonstrated that light also had a particulate nature.<br />

Experiments at that time showed that radiation could be considered as being made up of wave packets<br />

or photons. The energy associated with each photon can be expressed in the form<br />

E = hν (4.3)<br />

where h is Planck’s constant <strong>and</strong> equal to 6·625 × 10 −34 J s. Thus, it can be seen that the photons<br />

carrying the most energy are associated with the high frequency end of the spectrum, i.e. the γ -rays—<br />

photons associated with the radio spectrum have very low energy.<br />

For many observational circumstances, the flux of energy arriving from faint sources is such that<br />

it is the statistical r<strong>and</strong>om nature in the arrival of the photons that limits the quality of the measurement.<br />

In observations where the source of experimental noise errors is very small, it is perhaps the r<strong>and</strong>om<br />

arrival of photons that constitute the noise on the measurements. The accuracy of data recorded under<br />

such a circumstance is said to be limited by photon counting statistics or by photon shot noise. Inorder<br />

to be able to estimate the accuracy to which measurements of brightness or details within the spectrum<br />

can be obtained, it is necessary to know the photon arrival rate associated with the generated signal.<br />

For this reason, the strengths of observed sources are sometimes referred to in terms of photons s −1<br />

rather than in watts. Equation (4.3) is all that is needed to relate the two ways of expressing the amount<br />

of energy which is received by the observing equipment. More detail of this topic will be presented in<br />

Part 3.<br />

It may also be noted that in the zones covering the high energy end of the spectrum, neither<br />

wavelength nor frequency is used to describe the radiation. The more usual units used are those of the<br />

energy of the recorded photons. Thus, for example, features occurring in x-ray radiation are normally<br />

described in terms of photon energies of order 10 keV.<br />

Equation (4.3) describes the energy of a photon <strong>and</strong> this can be re-written as<br />

E = hc<br />

λ<br />

J. (4.4)<br />

By remembering the conversion of units such that 1 eV = 1·6 × 10 −19 J, the photon energy<br />

expressed in eV units is<br />

E[eV] = 6·625 × 10−34 × ν<br />

1·6 × 10 −19 or<br />

6·625 × 10 −34 × 3 × 10 8<br />

1·6 × 10 −19 . (4.5)<br />

× λ<br />

In order to determine the wavelength associated with a photon of some given energy, consolidation<br />

of the numerical parts leads to<br />

λ[m] =<br />

1·24 × 10−6<br />

E[eV]<br />

or λ[Å] =<br />

12 400<br />

E[eV] . (4.6)

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