Box-model calculation

There is some debate about what controls the magnesium concentration in seawater. The main input is rivers. The main removal is by hydrothermal processes (the concentration of Mg in hot vent solutions is essentially zero). First, calculate the residence time of water in the ocean due to (1) river input and (2) hydro-thermal circulation. Second, calculate the residence time of magnesium in seawater with respect to these two processes. Third, draw a sketch to show this box model calculation schematically. You can assume that uncertainties in river input and hydrothermal circulation are 5% and 10%, respectively. What does this tell you about controls on the magnesium concentration Do these calculations support the input/removal balance proposed above Do any questions come to mind Volume of ocean = 1.4 x 10 L River input = 3.2 x lO L/yr Hydrothermal circulation = 1.0 x 10 L/yr Mg concentration in river water = 1.7 X 10 M Mg concentration in seawater = 0.053 M. 

Atomic orbitals may be combined to form molecular orbitals. In such orbitals, there is a nonzero probability of finding an electron on any of the atoms that contribute to that molecular orbital. Consider an electron that is confined in a molecular orbital that extends over two adjacent carbon atoms. The electron can move freely between the two atoms. The C-C distance is 139 pm. (a) Using the particle in a box model, calculate the energy required to promote an electron from the n = 1 to n = 2 level assuming that the length of the box is equal to the distance between two carbon atoms, (b) To what wavelength of radiation does this correspond (c) Repeat the calculation for a linear chain of 1000 carbon atoms. 

Atmospheric reactions modify the physical and chemical properties of emitted materials, changing removal rates and exerting a major influence on acid deposition rates. Sulfur dioxide can be converted to sulfate by reactions in gas, aerosol, and aqueous phases. As we noted in Chapter 17, the aqueous-phase pathway is estimated to be responsible for more than half of the ambient atmospheric sulfate concentrations, with the remainder produced by the gas-phase oxidation of S02 by OH (Walcek et al. 1990 Karamachandani and Venkatram 1992 Dennis et al. 1993 McHenry and Dennis 1994). These results are in agreement with box model calculations suggesting that gas-phase daytime S02 oxidation rates are l-5% per hour, while a representative in-cloud oxidation rate is 10% per minute for 1 ppb of H202. 

Published box-model estimates of global average direct aerosol forcing by sulfate fall around —1 W m (National Research Council, 1996). Table 22.9 presents global mean values of the parameters in (22.74), along with estimates of the uncertainty associated with each parameter, as suggested by Penner et al (1994). Estimates of direct aerosol forcing by sulfates made in individual studies differ, even for box model calculations, because of dif-... 

The Bohr radius for the n = I level in hydrogen atom is 52.9 pm. Assuming that a = 2r for the one-dimensional particle in a box model, calculate the energies for the first three quantum levels in units of megajoules per mole. 

In this section, validation of the HOx chain reaction mechanism by the comparison of OH and HO2 concentrations obtained by recent field measurements and box model calculations, and the grasp of unknown OH-removing species by the field measurements of the OH reactivity are described. Meanwhile, although the comparison between the output of three-dimensional models with aircraft... 

Fig. 7.14 Comparison of HO2 and OH in the RISOTTO campaign at Rishiri, Japan, between the box-model calculation and observation (Adapted from Kanaya and Akimoln 2002)...

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