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conantee
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« on: December 31, 2009, 10:30:10 AM »

The energy levels of the hydrogen atom are given in terms of the principal quantum number n and a positive constant A by the expression
(A) A (n + \frac{1}{2})
(B) A (1 - n ^2)
(C) A (- \frac{1}{4} + \frac{1}{n ^2})
(D) A n^2
(E)  - \frac{A}{n^2}
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« Reply #1 on: December 31, 2009, 10:39:54 AM »

Unfortunately, there is nothing much about technique in this problem. Full-range quantum mechanics might not be helpful too since you may not solve the Schrodinger's equation on time. However, if you vaguely remember Bohr's theory of atom and transition spectrum of hydrogen (Lyman, Balmer, etc.). You might remember that there are many lines corresponds to energy levels. The lines gets closer and closer in the diagram at the top, where n is large. If you notice this, you can eliminate (A), (B), and (D) since they all represents energy levels which spread out when n is large. Now, for (C), it is not natural to have -\frac{1}{4} in there since if  n = 2, the energy blows up (you should know that 2 should be a good number of principle quantum number). The only choice you have now is (E).

This is an example that, even if you have just a small detail in your mind, you can do the exam without any calculation.

The correct answer is (E). 64 of 100 people got it correct. 
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