Solutions/Answers to Exercises
Exercise 1. Calculate the energy of the electron in the hydrogen atom if the electron is excited from n = 2 to n = 6. Calculate the wavelength when the electron transitions from n = 6 to n = 2.
\(\displaystyle h\nu\;=\;-2.179\times\;10^{-18}\;J\times\;\Biggl (\frac{1}{6^2}\;-\;\frac{1}{2^2}\Biggr )\;=\;4.87\times\;10^{-19}\;J\)
\(\displaystyle \frac{1}{\lambda}\;=\;1.097\times\;10^7\;m^{-1}\;\Biggl (\frac{1}{2^2}\;-\;\frac{1}{6^2}\Biggr )\;=\;2438\;m^{-1}\)
1/2438 m-1 = 4.10 x 10-4 m
Exercise 2.Indicate if energy is absorbed or emitted for the following electron transitions:
b) n = 3 → n = 1 emitted
c) from an orbit of radius 1.46 Angstroms to an orbit with radius of 0.768 Angstroms.
The electron is moving from a larger value of n to a smaller value of n. The energy is emitted.
Exercise 3. What is the energy, in kJ/mol, for an electron that transitions from n = 1 to n = ∞? This is the ionization energy for the hydrogen atom. Is the energy absorbed or emitted?
The energy of the electron in n = 1 is equal to -1312 kJ/mol. At n = ∞, the energy is 0. It would take 1312 kJ/mol of energy to remove the electron from a hydrogen atom.
Exercise 4. Calculate the wavelengths for the three lines in the infrared region of the hydrogen spectrum.
The first line is a transition from n = 4 to n = 3
\(\displaystyle \frac{1}{\lambda}\;=\;1.097\times\;10^7\;m^{-1}\;\Biggl (\frac{1}{3^2}\;-\;\frac{1}{4^2}\Biggr )\;=\;533264\;m^{-1}\)
1/533264 m-1 = 1.88 x 10-6 m.
The second line is a transition from n = 5 to n = 3
\(\displaystyle \frac{1}{\lambda}\;=\;1.097\times\;10^7\;m^{-1}\;\Biggl (\frac{1}{3^2}\;-\;\frac{1}{5^2}\Biggr )\;=\;780089\;m^{-1}\)
1/780089 m-1 = 1.28 x 10-6 m.
The third line is a transition from n = 6 to n = 3
\(\displaystyle \frac{1}{\lambda}\;=\;1.097\times\;10^7\;m^{-1}\;\Biggl (\frac{1}{3^2}\;-\;\frac{1}{6^2}\Biggr )\;=\;914167\;m^{-1}\)
1/914167 m-1 = 1.09 x 10-6 m.