A collection of atoms has 20% of the sample in a state 5.9 eV above the ground state. If these emit coherent radiation, what is the wavelength of the laser light produced? (c = 3*10^8 ms, h = 6.626*10^-34 J*s, 1eV = 1.6*10^-19 J Is simply hc/E but I keep getting 260 nm not 210 nm. 

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I double-checked the math and there must be something wrong with the way you're putting your numbers in, if you're getting 260nm instead of 210. Your procedure is correct - according to manipulations of Planck's Equation we should get E = (hc)/lambda, which can be rearranged to lambda=(hc)/E, where lambda...

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I double-checked the math and there must be something wrong with the way you're putting your numbers in, if you're getting 260nm instead of 210. Your procedure is correct - according to manipulations of Planck's Equation we should get E = (hc)/lambda, which can be rearranged to lambda=(hc)/E, where lambda is the wavelength, E is the energy of the photon and h and c are the planck and lightspeed constants.

Since the energy difference between the ground state and excited state is given as 5.9eV, we're assuming all of this energy is converted into radiation, and therefore E = 5.9eV, or (5.9)(1.6x10e-19) = 9.44x10e-19

hc = (6.626x10e-34)(3x10e8) = 19.878x10e-26

(19.878x10e-26)/(9.44x10e-19) = 2.10x10e-7, or 210nm.

I honestly can't tell where the error producing an answer of 260 is coming in, because it would require a pretty significant deviation from the given values on your input.

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