The allowed energies of a quantum system are 1.0eV , 2.0eV , 4.0eV , and 7.0eV W

Question

The allowed energies of a quantum system are 1.0eV , 2.0eV , 4.0eV , and 7.0eV

What wavelengths appear in the system's emission spectrum?
Express your answer using two significant figures.

Explanation / Answer

allowable transitions occur between energy levels; the wavelengths that appear will be the wavelengths of photons whose energies are equal to the energy differences between levels so you can get transitions whose energies are: 6ev (from 7->1) 5 ev(7->2) 3ev (there will be two ways of getting this; from 7->4 and from 4->1) 2 ev(4->2) 1 ev convert eV to Joules; 1eV=1.6x10^(-19)J and the relationship between wavelength in meters and energy is E = hc/L or L=hc/E where h is Planck's cst=6.62x10^(-34)Js and c=3x10^8m/s use these values of h and c with the individual values of E and find the characteristic values of L, or wavelength, for each allowable transition

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