Estimating Avogadro's number from skylight and airlight

Abstract

Naked-eye determinations of the visual range yield order-of-magnitude estimates of Avogadro's number, using an argument of Rayleigh. Alternatively, by looking through a cardboard tube, we can compare airlight and skylight and give another estimate of this number using the law of atmospheres.

Moles and Molecules

“…In the title it is an aggregation of 6.0…x10 23 particles such as molecules. The number is Avogadro's, derived many times and ways (e.g., Pesic, 2004; Robson et al, 2014; Shaxby, 1923; Slabaugh, 1969; Sunier, 1929), and of fundamental importance in chemistry. The mass of a mole of any such aggregate (e.g., of carbon atoms) equals the mass of a constituent particle when both are measured in appropriate metric units.…”

Overcast sky luminance is dependent on the physical state of the atmosphere below cloud level

“…the scale height of the molecular atmosphere) is about H m % 8 km, 27 while the scale height for the aerosol system is less than 2 km. 28 The altitude of clouds H is usually smaller than H m , so the molecular optical thickness …”

“…Similar results were also reported by Brunger and Hooper. 24 It is therefore impossible to explain a wide range of variable luminance profiles measured under overcast conditions by means of Equation (27). A serious disadvantage of the Moon-Spencer's formula is that it does not account for any parameter characterising the physical state of the atmosphere.…”

“…An altitude up to which a homogeneous molecular atmosphere would extend (i.e. the scale height of the molecular atmosphere) is about H m % 8 km, 27 while the scale height for the aerosol system is less than 2 km. 28 The altitude of clouds H is usually smaller than H m , so the molecular optical thickness Figure 3 The relative sky luminance of the overcast sky considering isotropic scattering in a non-absorbing undercloud atmosphere.…”

Discovering the Discrete Universe

“…The convergence of disperate methods of estimation, from Loschmidt's original result in 1865 to Einstein's various determinations in [1903][1904][1905], gave a strong reason to believe that there was something to the generic hypothesis. Here we will concentrate on a method of Rayleigh's, published in 1899 [1,2] 1 . This remarkable piece of physics enabled him to estimate Avogadro's number, based on a naked eye observation of Mount Everest.…”