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In the question where it asks to determine whether the change in energy will be positive or negative in the hydrogen atom that is excited by a photon with a wavelength of 102.557nm. . . I found the change in energy was 1.9x10^-18 and the E initial was -2.18x10^-18. For the E final I used the equation (change in energy = E final- Einitial) rearranged to be (E final =change in E + E initial). So, (1.9x10^-18)+(-2.18x10^-18) which equaled -2.4995x10^-19 but on the midterm solutions it says I'm supposed to get -0.24x10^-18. How did they get this?
I'm kind of lost so I'll just walk through the problem. Ok to start we have 1.94 *10-18 J for the change in energy by converting 102.557 nm to Energy which you have done. Then this value is equivalent to Efinal - Einitial. However, as you are subtracting a negative (the Einitial), it becomes Einitial - Efinal = DeltaE. Einitial is equal to 2.18 * 10-18J using hR/1. So you have 2.18 * 10-18J - hR/n2 = Delta E. You subtract DeltaE to both sides and add hR/n2 to both sides and get that hR/n2 is equal to the difference between Efinal and DeltaE. This difference should equal 2.43 *10-19J. You can then solve for n, which will be close to 3.
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