Chemistry 2720 Fall 2000 Test 2

Formulas and data can be found at the end of this paper.

Write your answers only in the booklet provided. Use extra pages at the back of the booklet for scratch work.

1.

State the number of orbitals of each of the following types which an atom can have: [4 marks]

(a)

5d

(b)

3f

2.

Briefly describe two phenomena which are explained by quantum mechanics but not by classical mechanics. [4 marks]

3.

What is the wavelength associated with a neutron ( $m=1.675\times 10^{-27}\,\mathrm{kg}$) whose speed is 8000m/s? [4 marks]

4.

Recall that graphite is made up of sheets of fused six-membered carbon rings. These sheets are 335pm apart. It is relatively easy to detect which direction is perpendicular to these sheets in a graphite crystal. Graphite can thus be used to monochromate X rays (i.e. isolate one particular wavelength). Palladium's $K_\alpha$ line has a wavelength of 58.9pm. At what angle would you need to turn the graphitic sheets of a crystal with respect to an incident X-ray beam to isolate the palladium $K_\alpha$ line? [5 marks]

Note: the most intense reflection corresponds to the lowest order of diffraction so monochromation of this reflection would be most effective.

5.

(a)

Since photons are particles (albeit massless), they must obey the uncertainty principle. Use this fact to derive a relationship between the uncertainty in a photon's position and energy. [5 marks]

(b)

Suppose that you manage to measure a photon's position to an accuracy of 1nm. What is the minimum uncertainty in the frequency? [4 marks]

6.

The first ionization energy of helium is 24.587eV. Although the Bohr formula cannot be applied to compute this value, one could define an effective nuclear charge by pretending that the Bohr formula does apply. Compute an effective nuclear charge on this basis. Give a physical interpretation to the value calculated. [6 marks]

7.

The Pfund series of the emission spectrum of hydrogen corresponds to transitions ending at n=5. Predict the wavelengths of the first four (lowest energy) lines of the Pfund series. [10 marks]

8.

(a)

What is the minimum speed of a protein molecule of molar mass 28000g/mol in a narrow capillary of length 1.5mm? Treat the molecule as a quantum mechanical particle in a one-dimensional box. [6 marks]

(b)

The average molar kinetic energy of molecules held at temperature T is $\frac{3}{2}RT$. If the above system is held roughly at room temperature (293K), are quantum mechanical effects likely to be important? [5 marks]

Formulas and Data

$1\,\mathrm{pm} = 10^{-12}\,\mathrm{m}$

$1\,\mathrm{eV} = 1.602\,176\times 10^{-19}\,\mathrm{J}$

$c = 2.997\,925\times 10^8\,\mathrm{m/s}$

$h = 6.626\,069\times 10^{-34}\,\mathrm{J/Hz}$

$N_A = 6.022\,142\times 10^{23}\,\mathrm{mol}^{-1}$

$R = 8.314\,510\,\mathrm{J\,K^{-1}mol^{-1}}$

$E_K = \frac{1}{2}mv^2$ p=mv

$n\lambda = 2d\sin\theta$

$c = \lambda\nu$

$E = h\nu$

$\Delta x\Delta p\ge \frac{h}{4\pi}$

E² = c²p² + m₀²c⁴

$p = h/\lambda$

For a particle in a box of length L, $E_n = \displaystyle\frac{n^2h^2}{8mL^2}$.

For a hydrogenic atom, E_n = -Z²R_H/n²with $R_H = 2.179\,874\times 10^{-18}\,\mathrm{J}$.