Calculate the probability that the electron will be found

Reference no: EM132424528

Questions - Need full detailed answers.

Q1. By considering the radial wave-functions of the 2s and 3s orbitals of hydrogen, deduce the number of nodes for each, and their location(s).

Q2. The wave-function for the ground state of a hydrogen atom is

ψ = (1/(πa₀³))^½e^-(r/a_0)

Calculate the probability that the electron will be found within a sphere of radius a₀ centred at the nucleus, given the following integral:

∫r²e^ar dr = e^ar/a (r² - 2r/a + 2/a²)

3. Using the data given below, calculate the fundamental vibrational wave number, v^~, the rotational constant, B^~_e, the moment of inertia, I, and the equilibrium bond length for ¹H³⁵CL, ¹H³⁷Cl, D³⁵Cl and D³⁷Cl.

H³⁵Cl		H³⁷Cl		D³⁵Cl		D³⁷Cl
P_J	R_J	P_J	R_J	P_J	R_J	P_J	R_J
	2905.72		2903.91		2101.29		2098.29
2864.6	2925.36	2862.85	2923.54	2079.93	2111.61	2077	2108.6
2843.06	2944.34	2841.41	2942.51	2068.93	2121.72	2066.08	2118.7
2821	2962.74	2819.46	2960.84	2057.71	2131.56	2054.85	2128.49
2798.39	2980.46	2796.86	2978.53	2046.28	2141.18	2043.47	2138.11
2775.24	2997.52	2773.71	2995.5	2034.64	2050.6	2031.82	2147.43
2751.52	3013.91	2750.01	3011.8	2022.79	2159.72	2020.04	2156.58
2727.3	3029.6	2725.8	3027.42	2010.74	2168.62	2008.01	2165.46
2702.57	3044.53		3042.36	1998.45	2177.25	1995.77	2147.05
2677.27	3058.84		3056.62	1985.99	2185.64	1983.37	2182.47
2651.54	3072.4		3070.08	1973.36	2193.74	1970.78	2190.52
				1960.52	2201.64
				1947.51	2209.27

Reference no: EM132424528

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