Hmm. In (a) there are two ways of getting all assignments wrong (if the correct one is 123, then these are 312 and 231) and there are 3*2*1 = 6 possible assignments. If his guesses are random this yields Pr(all wrong) = 2/6 = 1/3. In (b) I count 9 ways of getting all assignments wrong out of...
Yeah, I think I'll do that, although it gets rather complex in (b).
A slight problem though: when I count the combinations I get 3/8 in (b), but when I calculate it using the multiplication rule I get 1/4 :eek:
Hi. I'm a math instructor and this problem is given to 1. year economics students.
1. The problem statement
In an episode of the TV show "All in the Family", Mike claimed that he could identify different brands of cola by taste alone. He was challenged and presented with three glasses, one...
I've been staring at this for hours. Any hints?
Let the vector Y = (Y_1,Y_2,\dots,Y_k) have a multinomial distribution with parameters n and \pi = (\pi_1,\pi_2,\dots,\pi_k):
\sum_{i=1}^{k}Y_i = n, \quad \sum_{i=1}^{k}\pi_i = 1
Show that the conditional distribution of Y_1 given...
It's in the context of simple http://wwwchem.uwimona.edu.jm:1104/courses/CFT.html". I don't think there's any unobivious rules here, but I don't know...
I see your point. If we assume that every H2O molecule occupies one ligand space and does not interact with it's neighbors -- would I then be correct? It's an introductory course, so I assume there's no pitfalls.
Hi. I'm asked the following question:
What isomers does the complex [\text{Fe}(\text{H}_2\text{O})_6] give rise to? Is it optically active?
My answer to the first question would be 'none': The 6 identical H2O molecules are arranged in an octahedral fashion around the central Fe-atom, so...
c) Still in the dark. Can't relate these things to the activation energy... sorry.
f) Oxygen is more electronegative than nitrogen, so the OH-molecule has a greater dipole strength than the NH-molecule and therefore the hydrogen bond is stronger in the former case (O-H---O). Right?
Thanks...
Hi. I need help with (part of) this exercise:
c) By considering the differences in bonding determine which of the combustion reactions (in part a) I have written combustion reactions for the following hydrides: B2H6, CH4, NH3 and H2S) must be expected to have the lowest energy of activation...
It will shift to the right, so the solubility will go up (consistent with my result.) I should compute the I3- concentration and add it to the I2(aq) concentration to find the new solubility, right?
Hi. I'm preparing for a chemistry exam and I have trouble with this former exam problem:
The solubility of I_2\text{(s)} in water at 25ºC is 0.0013 M.
Calculate the solubility of I_2\text{(s)} in a 0.1 M solution of KI(aq) by considering this equilibrium:
I_2\text{(aq)}+I^-\text{(aq)}...
I have no idea, just quoting from the book, basically. Doesn't Li- and Cs-solids exist? I'm a lousy chemist, I know.
I would think that "quietly" means slow and "violently" means fast, so the statement is that the reaction rate of Cs + water is larger than the reaction rate of Li + water. I...
Hi.
How come that Cs reacts more violently with water than Li, when the enthalpy of hydration for Li is -520 kJ/mol while it is only -276 kJ/mol for Cs. More energy is released in the Li reaction, but still it reacts more quietly?
(EDIT: Oops, maybe this should be in the homework section?)
And yet another thing: even though the electrons doesn't interact, they still have to obey the Pauli exclusion principle, right? So we can't consider them independently after all, or...?
I see. Thanks.
Oh, just one more thing: how do you construct the state vector for the whole system from the individual single particle states? Is it like a tensor product (I'm unsure of the mathematics here.)
Hi,
I was just reading up on some QM, and I was wondering this: under what circumstances can you treat a bunch of electrons as occupying "single particle states", and when do you have to use one wavefunction depending on all the coordinates, psi(r1, r2, r3, ...)? Hope you know what I mean...
Oh, I think I get it now. I guess I was confused about the distinction between the axioms themselves and 'the model' to which they are applied. Thanks, everyone.
Hi.
I'm reading a simple introduction to groups. A group is said to be a set satisfying the following axioms (called the 'group axioms'):
1) Associativity.
2) There is a neutral element.
3) Every element has an inverse element.
4) Closure.
My questions is simply: why are they...
Hi.
Can anyone explain to me what spin-up effects are? The context is a waterwheel that consists of an ordinary wheel with papercups with holes in the bottom suspended along the rim. It is stated that for this wheel there are two sources of damping: ordinary frictional damping and "inertial"...
Hi.
How can I "experimentally" (by way of computer simulation) calculate an approximate value for the dimension of a fractal object? The object in question is the Lorenz strange attractor, which has a dimension between 2 and 3.
Also, I know there is a number of different ways to define...
Yes, that seems plausible, but is it always possible? One could imagine that it would be practically impossible if the sensitivity is critical enough. It usually isn't, I guess, since no one seems to care about it. It just seems like a problem as significant as the problem of the precise...
Hi.
I'm starting a project on chaos very soon and I was just wondering...
One of the distinguishing features of a "chaotic system" is the sensitive dependence on initial conditions. It is stated that if we knew the initial conditions with infinite precision we would also be able to...
Hi.
Can anyone explain the meaning of this formula from statistical physics to me:
S = -k\sum_r{p_r\ln p_r}
Ok, I know that S is the entropy, the p's are probabilities of some sort - but somehow this is not satisfactory :-)
Hi.
I'm reading a book on deterministic chaos, and an important distinction seems to be the one between dissipative and conservative dynamical systems. A dissipative system is defined as a system whose "phase space volumes shrink", whereas in a conservative system phase space volumes are...
Hi,
A very hot gas is enclosed in an oven with a small window. The gas molecules emits radiation at a characteristic wavelength. I assume that because of the thermal motion of the molecules the emitted wavelengths will form a spectrum of some kind (Doppler broadening.) I am trying to derive...
Yea, thanks. So if there is N atoms we would have Z_{tot} = Z^N?
I think what was confusing me was the fact that I used to think of the heat capacity intuitively as "the amount of energy needed to raise the temperature by 1 degree", and so, the heat capacity approaching 0 seems to imply that...
Hi.
I'm having trouble with this statistical physics thing again. I am given this exercise:
Problem 9 – A spin model
In a solid at temperature T the atoms have spin 1 so that the m quantum number takes on the values m = 0, ±1. Due to an interaction with the electrostatic field in the...
Hi. I've just started a course on statistical physics and the first assignment is this:
A system possesses 3 energy levels, E_1 = \epsilon, E_2 = 2\epsilon and E_3 = 3\epsilon. The degeneracy of the levels are g(E1) = g(E3) = 1, g(E2) = 2. Find the heat capacity of the system.
I've...
Hi,
I was just reading up on some astrophysics and I saw the line element (general relativity stuff) written in spherical coordinates as:
ds^2 = dr^2 + r^2(d\theta^2 + \sin\theta\d\phi)
I don't get this. dr is the distance from origo to the given point, so why isn't ds^2 = dr^2 without...
Ok, but two electrons in two different atoms can have the same set of quantum numbers without violating the exclusion principle. Why is this not a violation and when does it become a violation? (i.e. how close must the atoms be.) I hope you understand my question.
I see. Thanks for taking the time! This is off-topic, but how can we even talk about free space, when electrons are clouds that, theoretically, penetrate all space with some small amplitude.
And also, a totally unrelated question: What is the scope of the Pauli exclusion principle. It states...
Thanks, man. But how do I know that the cations and anions exactly touch (no free space between them), which is the assumption in your calculation (right?). Aren't they, like, hovering with some free space between them? (this is probably a stupid question :-)
Hi,
I have yet another problem with this diffraction thing. I have little clue on these questions:
e) The radius of the O^2- ion is assumed to be 0.126 nm. By x-ray diffraction experiments the dimensions of the unit cells for MgO, CaO, SrO and BaO has been determined to be 0.4213 nm...
Hi,
In the solid form FeO, CoO and NiO all has the NaCl-structure (simple cubic). In a series of diffraction experiments with x-rays (\lambda = 0.15406~\text{nm}) one found reflexes from the (111), (200) and (220)-planes with the following \theta-values (\theta is the angle in Bragg's law...
Ok, I see. The reaction is this (right?):
CO3^2- + CH3COOH -> HCO3^- CH3COO^-
How can I determine pH? All I know is that half of the CH3COOH is used up in this reaction.