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# Atomic Structure Essay Sample

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Answers should be submitted by 9:00 am on Monday September 24, 2012 in the box provided. Please write your ID number and Laboratory day clearly on your script. 1. Give an expression for the Balmer-Rydberg equation in terms of wavelength Î», the Rydberg constant R, and the integers m and n where m < n.[3] a. Using the equation calculate the wavelength (in nanometers) of the first line of the Lyman series (m = 1).[3] b. To which region of the electromagnetic spectrum does this wavelength correspond ?[1] c. Using the Balmer-Rydberg equation, at what value of n does the red line (wavelength = 656.3 nm) in the Balmer series of the hydrogen emission spectrum occur.[5] 2. Calculate the wavelength of the following:

a. A photon of energy 2.89 x 10-19 J[2]
b. An electron travelling at 1/5 of the speed of light[3] c. A 70 kg man running a 100 m sprint in 9.84 s.[3] i. In parts b. and c., how does the wavelength compare to the region in which the â€śparticleâ€ť is confined?[2] ii. Based on your answer in part c, how significant is the manâ€™s wave-like properties? Briefly explain.[1] 3. Write the expression for the Heisenberg Uncertainty Principle (HUP).[2] a. Determine the uncertainty in the path of flight of an 8.040 g bullet if its velocity is 360 Â± 1 ms-1. (Hint: the mass is known with high precision therefore Î”mv = mÎ”v)[3] b. Determine the uncertainty in the position of an electron if the velocity is 5.80 Â± 0.02 Ă— 106 ms-1.(Use the hint given above)[3] i. How does the error in the position of the â€śparticlesâ€ť in a. and b. compare to the space they occupy?[2] 4.For an electron of principal quantum number n = 4, what are the possible values for l and ml?[6] 5.Sketch the shapes of the 1s, 2s and 2p orbitals.[3] Total 42 marks

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