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hvi-

where here RH is the Rydberg constant for atomic hydrogen given by

2n2e4m

Rh ch3

where e is the electron charge and m the reduced mass of the electron-proton system of H, so that ft.RHc is equal to 13.60 eV. Thus, if we set n = 1 and nj = to then the energy difference is the ionization limit that is equal to 13.60 eV and corresponds to radiation at the wavelength 912 A. Generally, the ionization Wavelength (nm)

FlG. 5.3. The mean solar spectral irradiance, Sq\ above the atmosphere of the Earth, corresponding to a solar constant 1366 W m"2. (Data from Gueymard 2004)

limit from the n level is equal to hRHc/n2. In Table 5.4 are shown the first three transitions and the ionization limit for the Lyman, Balmer and Paschen series.

In thermodynamic equilibrium, we can use the Boltzmann distribution to calculate the ratio of the population of H atoms in the second level and that in the ground state to obtain an idea of the strength of the Lyman-a flux at any given temperature from

ni gi where the statistical weight of each level is given by (2s + 1)(2/+ 1), where s = i corresponds to the electron spin quantum number and l the orbital quantum number. For the ground state, n = l,l = 0 and so g1 = 2, whilst for the first excited state n = 2,l = 0 or l, and hence g2 = 8. For the hydrogen atom g = 2n2. Thus, at T = 6000 K, n2/n1 = 10"8, while at T = 20000 K the value of the ratio is 0.01. Hence, in the solar chromosphere there is significant Lyman-a emission. As we shall see when we look at the photochemistry of the atmosphere, solar Lyman-a radiation plays a significant role in the dissociation of water vapour and oxygen molecules in the Earth's mesosphere, while Lyman-,3 plays an important role in the ionization of nitrogen and oxygen in the Earth's thermosphere. In Fig. 5.5 is shown the Lyman-a line profile normalized to a quiet Sun value for the total flux of 3.5X1011 photons cm"2 s"1.

ionization limit

 i . i . i Paschen i i L Balmer i Lyman

FIG. 5.4. Spectral line series of the H atom.

 Series Transition Energy (A) Label Lyman 2 1216 a (ultraviolet) S 1026 3 4 972 Y TO 912 limit Balmer 2 656S Ha (visible) S 4861 H3 4 4S40 Hy to S646 limit Paschen 2 18751 P4 (infra-red) S 12818 P5 4 109S8 P6 1 8204 limit

5.2.4.1 Ultraviolet flux variations We have seen that sunspots produce small variations in solar luminosity, however, the concomitant magnetic activity can produce large variations in the ultraviolet flux. For the present Sun, the solar cycle minimum to maximum variation in the ultraviolet flux above 200 nm is small, typically about 10%, while the variation at Lyman-a can be a factor of about 2. The quiet-sun Lyman-a flux is about 3.0 ±0.1 xlO11 photons cm"2 s"1, while measurements over cycles 21 and 22 give a solar maximum value of 6.75 ±0.25x10" photons cm"2 s"1. Wavelength (nm)

FlG. 5.5. The solar Lyman-a irradiance above the atmosphere, averaged for quiet Sun conditions for solar cycle 23. (Data from Lemaire et al. 2005) 