# Midterm 2

- Page ID
- 50496

**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 CO_{2} follows Michaelis-menten enzyme kinetics with K_{m}=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 CO_{2} 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 K_{m}, 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?