4. An electron in a H atom can relax (go from an excited state to its ground sta

Question

4. An electron in a H atom can relax (go from an excited state to its ground state) fromn 3 to either n 2 or n-1. Each transition releases a photon. (2 points each) a. Which transition (3- 2 or 3 1) will give off the photon with the greater energy? b. Which transition will emit the photon with the longer wavelength? 5. Consider our definitions of continuous vs quantized (Is the variable limited to discrete values?). ldentify the following as either continuous or quantized. (1 point each) a. Jelly beans in a jar b. Wavelength of electromagnetic radiation c. Length of a growing bean vine d Set of integers 6. The location of an electron in an orbit is defined by 4 quantum numbers. What do each of these quantum numbers tell us about that orbit? (Limit your answer to 1 line; 2 points each) a. n b. c. m d. m,

Explanation / Answer

4.

a) In an hydrogen atom, each energy level's energy increases propotional to the square of n. The energy emitted by an electron relaxing from an higher energy state to a lower one is given as the difference between the two energy levels. Thus if an electron from n=3 goes to n=1, it will emit a photon with more energy than when it relaxes from n=3 to n=2.

b) E = hc/wavelength (represented as lambda). Thus one can observe that energy of a photon and its wavelength are inversely propotional to each other. Therefore one can deduce that the photon with higher energy will have a lower wavelength and a photon with lower energy will have a higher wavelength. So the lower energy transition, from n=3 to n=2 will have a longer wavelength photon than that produced by relaxation from n=3 to n=1.

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