Steps involved in photon emission What are the detailed steps involved in the emissions of a photon, for example, when an electron drops to a lower energy level?  How well do we understand the production of the photon in this example?  Any good reference material I can study?
How do electrons jump orbitals? My question isn't how they receive the energy to jump, but why.  When someone views an element's emission spectrum, we see a line spectrum which proves that they don't exist outside of their orbitals (else we would see a continuous spectrum).  Electrons can be released in the form of beta decay, thus proving that they are capable of traveling outside of orbitals contrary to the statement my teacher said that they stay within orbitals. Then, to add to the confusion, the older model of rings floating around a nucleus has, from what I can tell, been outdated, which would support this model. My teacher's explanation was that the electrons made a quantum jump of some kind. How do electrons move between orbitals or do we know how they jump, excluding the reason that energy causes them to jump, and why are positrons formed sometimes instead of electrons in Beta decay?  When I'm asking "how do electrons jump" I would like to know how an electron can jump between each orbital such as how it moves and how it knows where to jump since it appears to be a jump where the electron doesn't slow into a orbital position. Specifically how they jump what is this Atomic electron transition, I understand that they jump and that they do this through absorbing and releasing energy but what is this Atomic electron transition other than what is already on the wikipedia article .
Under what condition we can interchange order of a limit and a summation? Deleting comment removes "Add comment" link on Mobile If I delete a comment on the mobile version of the site (at least if it's the only comment on an answer), the "Add comment" link will vanish along with the comment, so I have to reload to leave another comment.     but got declined as , which is why I'm reposting this (as it may well be a new bug with the same symptoms).  I'm using Firefox 32.0.3 on Android. How to treat differentials and infinitesimals? In my Calculus class, my math teacher said that differentials such as $dx$ are not numbers, and should not be treated as such.  In my physics class, it seems like we treat differentials exactly like numbers, and my physics teacher even said that they are in essence very small numbers.   Can someone give me an explanation which satisfies both classes, or do I just have to accept that the differentials are treated differently in different courses?  P.S. I took Calculus 2 so please try to keep the answers around that level.  P.S.S. Feel free to edit the tags if you think it is appropriate. My Ubuntu 12.04 was normally updated through the Update Manager, something about gtk. Then I rebooted and now all that shows after the splash screen is a blue screen that only shows the cursor. When should I start an LLC for my side work? I am doing quite a bit of sidework this year and wondering at what point would it be a good idea to "start a business" and bill through that. I have this picture:  (I have the original in Pixen and could export it to several different formats. I went with PNG though since it's lossless.)  When I open my picture in Preview (OS X) and zoom in, it looks fine. The characters have extremely sharp boarders between them and the background. However, when I put it into my LaTeX document, compile it to a PDF (using TeXShop) and then zoom in, it suddenly have gotten blurry (see screenshot: ).  Minimal working example:  \documentclass[12pt]{article} \usepackage{graphicx} \begin{document} \includegraphics[scale=1]{fig1.png} \end{document}   In the end, I would like to be able to scale the picture freely without there being any blurring at all. What is your Instagram password when signing in using Facebook? Do this:   On your phone, create an instagram account using Facebook log in. Now on your desktop web browser, log in using Facebook connect.  Now go to delete your account - edit profile -> I'd like to delete my account.    It will ask for your password.   But you never gave it a password in order to create the account.   I tried using my Facebook password, but that didn't work.   Any ideas? The Instagram account management seems quite broken. Note: this post is different to , which just cites part from somewhere else, without any further analysis and thinking. Furthermore, none of the answers to that post answers my question - the situations where &quot;will (going to) be doing&quot; is more appropriate.   I will be participating in IELTS test next Tuesday afternoon.  In an online class, the teacher says the following at the beginning of the lesson.  I will be using NotePod (pointed out by red rectangle) to write relevant points we talk about today.   I guess &quot;will be using&quot; is more appropriate than &quot;will use&quot; there, right?  A  explains  This &quot;tense&quot; is used for reporting a scheduled activity with special focus on its timing— as if one is standing in the future and experiencing the flow of the time. The focus is on the temporary, ongoing, or repetitive nature of the activity.   I understand the grammar rules of those verb tenses and the difference between this group  I am going to drive home tomorrow.   I am going to be driving home tomorrow.  The former is just convey my activity in the near future while the latter probably makes an implication that &quot;don't disturb me as I am driving in that time&quot; However, in the following situations, I don't see the difference between 2 verb tenses.  Welcome back to this class. Today's lesson is for the IELTS students who are going to be taking the IELTS test. it's for everybody to be honest with you. this lesson is useful for anybody who needs to do some writing.   who are going to take the IELTS test ... Revision history suggests that I edited the post body, whereas I didn't I was doing some re-tagging and I noticed that the automatically generated revision comment says that I edited the post body where I only edited the tags. Evaluate the limit : $$\lim_{n \to \infty } {1 \over {\sqrt n }}\left( {1 + {1 \over {\sqrt 2 }} + {1 \over {\sqrt 3 }} + \cdots + {1 \over {\sqrt n }}} \right)$$  I can use the sandwich principle, certain convergence criteria, Cesaro mean theorem, limit arithmetic.. things around this area.  Any help would be greatly appreciated, thanks!  Sorry for not elaborating more at the beginning, rookie first-post mistake I suppose. :) Paradox of General Comprehension in Set Theory, other than Russell's Paradox As is well known, the General Set Comprehension Principle (any class is a set) leads to the Russell Paradox (the class $x \notin x$ cannot be a set). As a result, set theories must restrict the Comprehension Principle to avoid self-reference. For example, in the case of ZFC, this is done by enumerating a small list of "safe" comprehension schema such as Separation.  Does General Comprehension lead to other types of paradox than Russell's? Or is this basically the only thing that can go wrong? Can we define tension in a string as the reactive force produced in a string being pulled at both ends? In my textbook, the definition of tension was given that  is the reactive force which exists when string is being stretched at its both end. After it there was a case given that to calculate acceleration and tension produced in string while it's attached with different masses at both its ends and passed over a frictionless pulley. First body is being hung and second is placed over horizontal frictionless surface with relatively smaller mass. It is given in my book that there are three forces acting on the body placed on horizontal smooth surface viz., Weight of body, the reaction force to weight and tension in string pulling body towards pulley's wheel. How can there be tension in string according to the definition given my book however there is no acting force (pulling force) on the body that pulls it away from wheel.  There are different definitions for tension. The one in our book is creating problem however second one, that is, " tension describes the pulling force exerted by each end of a string, cable, chain, or similar one-dimensional continuous object " is al right.  Since acceleration is lowered due to Tension then acceleration produced in the body must be given by, $a=\frac{Net-Force}{m}$ $=&gt;$ $a=\frac{m_1g-T}{m_1}$ since $W_1$ $&gt;$ $T$.  If tension in string is the reactive force to the weights pulling the string apart then according to Sir Isaac Newton, $W_1=W_2=T$. If it is given that component of acceleration perpendicular to the velocity of a body has a constant, non-zero magnitude, how can we mathematically prove that the trajectory of the body will be circular?   I have basic knowledge of calculus, vectors and co-ordinate geometry. I can prove that the trajectory of a body in projectile motion is parabolic. I tried to follow a similar method to get an equation of circle but couldn't succeed. I tried forming parametric equations of x and y in terms of time t (the way we proceed when proving the parabolic path of a projectile) but could not reach the conclusion.  Edit: I have edited the question in order to improve it. However I still can not share my work on this question as I had asked the question almost 6 months ago and now I can not find where I tried solving it. Sincerely sorry for that. What's the "official" explanation for Harry's (and everyone else's) absence from muggle school? So a bunch of kids all of a sudden "go missing" from school.  Harry Potter having attended school for a couple of years before starting at Hogwarts, one semester just doesn't show up.  How is this solved? What do parents say when a school teacher calls and wonders where their pupil is?  I assume that Hogwarts isn't an officially recognized school (though perhaps it is?), and due to education being compulsory, someone would do the math and find that low-hundreds of kids go missing in the transition from primary to secondary school every year. Can I choose to delay my turn in combat? Infinite DeMorgan laws Let $X$ be a set and $\{Y_\alpha\}$ is infinite system of some subsets of $X$. Is it true that: $$\bigcup_\alpha(X\setminus Y_\alpha)=X\setminus\bigcap_\alpha Y_\alpha,$$ $$\bigcap_\alpha(X\setminus Y_\alpha)=X\setminus\bigcup_\alpha Y_\alpha.$$ (infinite DeMorgan laws)  Thanks a lot! Are we slightly lighter during the day and slightly heavier at night, owing to the force of the Sun's gravity? List of lists changes reflected across sublists unexpectedly I needed to create a list of lists in Python, so I typed the following: my_list = [[1] * 4] * 3  The list looked like this: [[1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1]]    Then I changed one of the innermost values: my_list[0][0] = 5  Now my list looks like this: [[5, 1, 1, 1], [5, 1, 1, 1], [5, 1, 1, 1]]    which is not what I wanted or expected. Can someone please explain what's going on, and how to get around it? Direct formula for area of a triangle formed by three lines, given their equations in the cartesian plane. I read this formula in some book but it didn't provide a proof so I thought someone on this website could figure it out. What it says is: If we consider 3 non-concurrent, non parallel lines represented by the equations : $$a_1x+b_1y+c_1=0$$ $$a_2x+b_2y+c_2=0$$ $$a_3x+b_3y+c_3=0$$ Then the area of the triangle that these lines will enclose is given by the magnitude of : $$\frac{det\begin{bmatrix}a_1 &amp; b_1 &amp; c_1\\a_2 &amp; b_2 &amp; c_2\\a_3 &amp; b_3 &amp; c_3\end{bmatrix}^2}{2C_1C_2C_3}$$ Where $C_1,C_2,C_3$ are the co-factors of $c_1,c_2,c_3$ respectively in the above matrix.  What I'm wondering is, where did this come from? And why isn't it famous? Earlier we had to calculate areas by finding the vertices and all but this does it in a minute or so and thus deserves more familiarity. Where does the extra kinetic energy of the rocket come from?