Assignment Task: Need full detailed answers.
Problem 1: 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).
Problem 2: 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:
∫r2ear dr = ear/a (r2 - 2r/a + 2/a2)
Problem 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
|
|
PJ
|
RJ
|
PJ
|
RJ
|
PJ
|
RJ
|
PJ
|
RJ
|
|
|
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
|
|
|
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