Problem 1 (2 points each = 20 points total)
MARK the following statements as TRUE or FALSE.
- The Pauli Exclusion Principle states that two or more electrons in a single atom must have the same four quantum numbers.
- At absolute zero, all intermolecular and intramolecular motion has ceased.
- The square of the wavefunction is measure of the energy of the wavefunction.
- The Bohr Principle states that an atom is wavelike only when it has enough mass to exceed the Bohr radius.
- Amino acids are never part of the active site of an enzyme?
- The number of nodes in a wavefunction is typically correlated to the energy of that wavefunction.
- According to Einstein’s Law of photoelectron effect in a primary photoionization process of a metal, each electron is generated by the absorption of a single photon.
- Enzymes can make a reaction go faster by reducing DG for the reaction.
- Hydrogen-like wavefunctions are derived from solving the Schrodinger equation for a charged nucleus with a single moving electron.
- The particle in the box model predicts that the particle has a small probability to be found outside the box as long as the potential walls surrounding the box are of finite height.
Problem 2 (10+10=20 points)
2A) What is the energy of a particle with mass of 2.3 x 10-27 kg that is confined in a one-dimensional box of 50 Å length? Assume that the particle is in the third energy level.
2B) What is the wavelength of a photon released during a transition from level three to level two in above system?
Problem 3 (10 + 5 points = 15 total)
3a) The speed of a hydrogen atom is 350 km s-1. If the uncertainty in its momentum is 0.01%, what is the uncertainty in its location? If a hydrogen atom has a diameter of 1.4 Å, how large is this uncertainty compared to its size (i.e., in percent?)
Problem 5 (10 points each = 20 points)
B) A reaction that consume CO2 follows Michaelis-menten enzyme kinetics with Km=0.001 M, and the initial concentration of substrate=0.840 M. After 2 seconds, 5% of the substrate has been converted to product[DL1] . How much CO2 will be converted after 10 and 60 seconds?
3B) When 2 x 10-10 mol is added to a 1-L solution containing its substrate at a concentration one hundred times the Km, it catalyzes the conversion of 75 µmol of substrate into product in three minutes. What is the enzyme’s turnover number (turnover rate)?
Problem 6 (2 + 5 = 8 points total)
Answer the following questions using the diagrams shown for enzymatic catalyzed reactions.
- Which enzyme is providing the least acceleration in relationship to the non-catalyzed reaction?
- Which enzyme is providing the greatest acceleration in relationship to the non-catalyzed reaction?
- When comparing enzymes 1 and 4, which will be faster?
- When comparing enzymes 2 and 3, which will be slower?
Problem 7 ( 6 + 3 + 3 = 12 points)
7A) How many electrons in a hydrogen atom can occupy the wavefunctions with the following values of l:
- l =0
- l =3
- l =5
7B) What is the probability of finding a particle outside a box (choose either: 0, 1 or in-between)
- with finite potential walls and why?
- with infinite potential walls and why?
7C) What is the probability of finding a particle exactly in the middle of a box (with infinite potential walls) when excited to the n=1 state?
Problem 8: 10 points
The diffraction phenomenon can be observed whenever the wavelength is comparable in magnitude to the size of a slit opening. How fast must your instructor, weighing 92 Kg, run to diffract through a door 1 m wide?