## Getting a feeling for the numbers

1. What is the energy of a 'typical' photon?

Calculating the energy of a photon of wavelength X = 500 nm (in the middle of the visible spectrum), tf = hf = hi = 6-63x 10~34 Js X3X 108ms~1 = 3.98 x ^j X 500 x 10 m

On the macroscopic scale this is a tiny amount of energy; quantisation has a negligible effect at the macroscopic, or 'household', level. At the atomic level, however, it plays a major role.

2. How many photons do you need to activate the human eye?

The maximum sensitivity of the human eye is about 2 x 10-18 W. How many photons per second of wavelength 500 nm does this represent?

The energy of each photon is 3.98 x 10-19 J. Therefore the eye is sensitive to 2 x 10-18/3.98 x 10-19 = 5 photons.

If you are happy to accept that Planck's quantisation hypothesis leads to the correct formula for the black-body spectrum, skip to Section 11.5.5, 'A reactionary hypothesis'.

If you are curious to follow the fascinating story of how the formula appears out of the mathematics, read on.

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