Outlier

An electron in the ground state of a silicon atom has the quantum numbers (3,1,-1,+1/2) and absorbs infrared radiation of wavelength 1095 nm. To which energy level does the electron move?

An electron in the ground state of a silicon atom has the quantum numbers (3,1,-1,+1/2) and absorbs infrared radiation of wavelength 1095 nm. 

My thoughts are that I first need to calculate the energy that will be absorbed by the atom using E = hv where h is Planck's constant and v is the frequency of the infra red wave. To get v, I use c = v*lambda where  c is the speed of the infrared wave and lambda is the wavelength. I assume that c will be the same as the speed of light (not sure if this is a valid assumption). 

So 2.998 x 10^8 = v * 1095 x 10^-9 => v = 2.74 x 10^14 Hz

Hence E = 6.626x10^-34 * 2.74 x 10^14 = 1.82 x 10^-19 J

However, I don't know how to relate this back to the quantum numbers since I'm not sure how to interpret them correctly. I recall that each level is discrete and that the electron will absorb all of the energy provided by the radiation so it will jump to the level corresponding to the energy level, but I'm not sure how to go about calculating that. 

I know that B will have the least upper bound property if every non-empty subset of B which is bounded from above has a supremum in B. However, I am a bit lost on how to go about showing this.

I let S = {x ∈ Q: x^2 ≤ 7} be a subset of B. Now S has an upper bound in B but does not have a supremum in Q since no values of a + b√2 + c√3+ d√5 = √7 exists for a, b, c, d ∈ Q.

Is this correct?

I have already shown that A is denumerable by defining a bijective function from Z to A (since Z is denumerable):

Define f: Z -> A by f(z) = (z, -2z).I can similarly define a bijection from N to B to show that B is denumerable, but I think the question wants me to define a bijective function from A to B. I am not sure what this bijective function could be.I was thinking of a piecewise function where f(x) = -x for x > 0, f(x) = x for x < 0 and f(x) = (x - 1, 2x+ 1) for x = 0. But this seems very complicated since that showing A is denumerable is worth more points than showing that B is denumerable.

How do I implement a survey where a user, having selected an option from a main menu and answered the questions based on that option, can return to a menu and select additional options? I want all answers to be recorded. So the user can select one or more options, but not at once from the main menu. Only if he answers the questions from the option first. 

I'm trying to predict hurricane count in the Caribbean using a poisson regression, and I am following a book by Elsner and Jagger which gives details on how to do so using R.

Their book is concerned with hurricane landfalls in the US. However, since my area of interest is further south of this, I'm wondering if the environmental variables described in the book still apply.

The variables are:

1) Atlantic sea surface temperature (SST) derived from Atlantic Multidecadal Oscillation as an indicator of oceanic heat content:

https://www.esrl.noaa.gov/psd/data/correlation/amo...

2) Southern Oscillation Index (SOI) related to El Nino-Southern Oscillation (ENSO) as indicator of wind shear:

https://climatedataguide.ucar.edu/sites/default/fi...

3) Northern Atlantic Oscillation (NAO) as an indicator of steering flow:

https://crudata.uea.ac.uk/cru/data/nao/nao.dat

4) Sunspot number (SSN) as an indicator of upper air temperature:

https://www.esrl.noaa.gov/psd/gcos_wgsp/Timeseries...

Now, I ran my poisson regression model and found that NAO and SSN were statistically insignificant (p-values were greater than 0.4).

SST was significant with p-value less than 0.01 and SOI was significant with p-value less than 0.05.

Are these environmental variables suitable? They seem to deal with the North Atlantic and I'm therefore not sure if they would affect the southern Caribbean as much as the US.

Show that the integral (from -pi/2 to pi/2) of

tan^2 (x) (pi^2/4 - x^2) dx

is infinite,

But integral (from -pi/2 to pi/2) of

|tan x| ((pi^2/4 - x^2) dx is finite.

Y~B(n,p), n = 1000. Use the normal approximation to the binomial to approximate P(|Y/n - p| ≤ 0.05) and compare with the bound using Chebychev's inequality. If Y = 700, determine the corresponding confidence interval for p.

I've tried using the definition of the continuity of a function to ultimately get

|f(x) - f(c)| < ɛ and |g(x) - g(c)| < ɛ for all ɛ > 0, where x, c ∈ (a,b).

I know that to show the set in question is open, I have to show that there exists an x ∈ (a,b) such that for all ɛ > 0, N (x,ɛ) is a subset of (a,b) such that f(x) < g(x).

But I don't really see how I can reach to this conclusion.

So, I want to know the general temperature of the subsurface at 16,000 ft. I decided to use the average geothermal gradient of 15 degF per 1000 ft and a standard temperature of 60 degF to obtain a temperature of 285 degF at a 16,000 ft depth.

But I realize that the temperature of boiling water is 212 degF.

Is it plausible that the water at that depth in the subsurface is basically steam then?

I want the date to be automatically formatted to a number such as in the following example:

12/31/1993 (original date format) to 19933112

Is an automatic format possible? I have hundreds of these that need to be formatted!

What are some good movies to watch? I like movies of most genres, once there are good plots.

I find that many movies that are critically acclaimed (such as the Godfather, Shawshank redemption etc) don t really interest me, although I appreciate their quality.

I m just looking for fun and exciting movies but I m not sure where to look.

Question: A manufacturer claims that the average tensile strength of thread A exceeds the average tensile strength of thread B by more than 12 kg. To test this claim, 50 pieces of each type of thread were tested under similar conditions. Type A thread had an average tensile strength of 86.7 kg with a standard deviation of 6.28 kg, while type B thread had an average tensile strength of 77.8 kg with a standard deviation of 5.61 kg. Test the manufacturer's claim using a 0.05 level of significance.

Problem: Which of these should be the correct hypothesis tests?

H0 : uA - uB = 12

H1: uA - uB < 12

OR

H0: uA - uB = 12

H1: uA - uB > 12

The reason for my confusion is that the null hypothesis must always be represented by an equality, and the alternate hypothesis is always the exact opposite of the null. This would then mean that the second set of hypotheses are true. But the test statistic turns out to be negative, hence I am led to believe that the test should be a left tail instead, as indicated by the first set of hypotheses.

Which set of hypotheses is the more logical one to use, and why?

Let Y= √X. If X follows an exponential distribution with mean theta, find E(Y)

The top of an anticline has an area of 850 acres and the surface area of the surrounding rock connecting the base to the top is 800 acres. The height of the anticline from the base to the top is 80 ft. Is it possible to calculate the volume of this structure with this information? The area of the base is unknown.

I have been given an assignment to log a sedimentary outcrop and thereby determine the facies present.

In one of my logs, I have deduced that the facies which exist are as follows:

1) massive, medium grained, well-sorted sandstone

2) Medium grained sandstone with clay rip up clasts

3) Mudstone with planar laminae of fine-grained sand

4) Medium grained sandstone with few symmetrical ripples and clay drapes.

I'm not sure how to go about interpreting these facies. Can anyone perhaps give me an indication of the processes that deposited and preserved these facies and the conditions in which they were deposited? Any help would be greatly appreciated!

By using the transformation x + y =u, y = uv.

Show that double integral:

∫0 to 1∫0 to 1-x (ey/x+y)dy dx = (e-1)/2

I just need to know what the limits would transform to (in terms of u and v) with an explanation, and then I can take it from there. I ve already found the Jacobian and I know how to express the region in terms of u and v.

Let G be a cyclic group of order 20 generated by an element a, and let H be a subgroup of G generated by the element a^4. List all the cosets of H in G. It is known that H is normal. Give the operation table for the quotient group G/H.

Prove or disprove that H (the set of elements h that are a member of G, such that h^-1 = h) is a subgroup if the group G is abelian.

So clearly there exists an inverse for each element h in H since h^-1 = h.

But how do we show whether H has an identity and is closed?

h.h^-1 = e = h.h^-1 = h.h

Of course, h.h = e so h.h is a member of H and this is closure. But how do I show that h.h exists in H?