Calculation QM 2 (qm-02) Electrons of the solar wind reach Earth after a flight time of about 30 hours, where they can produce polar lights. In the case of polar lamps, green illumination is predominant, caused by the stimulation of oxygen at λ = 557.7 nm. Calculate that the kinetic energy of the electrons of the solar wind is sufficient to stimulate oxygen. Note: The distance between Earth and the Sun is 150 million km Note 2: m(e–)= 9.1·10-31 kg

  Exercise: qm-02    

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Electrons of the solar wind reach Earth after a flight time of about 30 hours, where they can produce polar lights.
In the case of polar lamps, green illumination is predominant, caused by the stimulation of oxygen at λ = 557.7 nm.
Calculate that the kinetic energy of the electrons of the solar wind is sufficient to stimulate oxygen.
Note: The distance between Earth and the Sun is 150 million km
Note 2: m(e^–)= 9.1·10^-31 kg

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Solution:

1. · General idea: the kinetic energy must correspond to at least excitation energy
2. · E_kin = ½ · m·v²
3.     = ½ · 9.1·10^-31·(1.5·10¹¹m/(30·3600))^2 = 8.8·10^-19 J
4. · E_A = h·c/λ = 6.626·10^-34Js·3.0·10⁸/557.7·10^-9 = 3.6·10^-19 J
5. · E_kin / E_A = approx. 2.4
6.     i.e. there is more kinetic energy than excitation energy

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