Solar energy strikes the top of the Earth's atmosphere at 343 W m-2. About 30 per cent of this energy is reflected directly back into space. The Earth-atmosphere system absorbs the remaining energy and re-radiates it into space as black body radiation given by Stefan-Boltzmann Law: O = oT* , o = 5.67 × 10-8 Wm-²K-4, where T is the temperature. Assuming that the arrangement has come to equilibrium, (i) what is the average black body temperature of the Earth? (ii) Calculate the wavelength at which the black body radiation from the Earth is at a maximum? (Hint: At Equilibrium the total energy emitted is equal to the total energy absorbed.)

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de Broglie Equation

The sketch of matter waves is drawn below: