We know the electron that jumps from a higher energy to a lower energy state emits its energy in the form of electromagnetic radiation. What will happen if a proton jumps from a higher energy state to a lower energy state?
When incident light passes through a hydrogen gas, for example, does it have 50% chance (since it's a 1:1 ratio of protons to electrons) of getting absorbed by the proton? Any chance at all? If no, why not? Does a proton have a "bandgap"? If yes, what happens when a photon is absorbed by a proton?
Undefined control sequence error on \fancy@reset, \f@ncyolh and \f@ncyorh when using newlfm class Showing that $ \sum_{n=1}^{\infty} \arctan \left( \frac{2}{n^2} \right) =\frac{3\pi}{4}$ Why is the Mann–Whitney U test significant when the medians are equal? I've received a results from a Mann-Whitney rank test that I don't understand.  The median of the 2 populations is identical (6.9). The uppper and lower quantiles of each population are:   6.64 &amp; 7.2 6.60 &amp; 7.1   The p-value resulting from the test comparing these populations is 0.007. How can these populations be significantly different? Is it due to the spread about the median? A boxplot comparing the 2 shows that the second one has far more outliers than the first. Thanks for any suggestions. Adding popup message box before tool execution with ArcPy and ArcMap I want to add a box message to pop up before execution of a button tool. When I click a button which will do geoprocessing, I want a box to appear on view before processing with message that I am about to do xxx processing. How do I do it? Last upgrade crashes network manager (no internet connection, no applet) While upgrading today, something caused my wireless network manager to disappear. Not even connecting via wired connection.  This error is being shown by files:  **(nm-applet:2716): WARNING **: Could not initialize NMClient /org/freedesktop/NetworkManager: The name org.freedesktop.NetworkManager was not provided by any .service files   (nm-applet:2716): nm-applet-WARNING **: Error connecting to ModemManager: Error calling StartServiceByName for org.freedesktop.ModemManager1: GDBus.Error:org.freedesktop.DBus.Error.Spawn.ExecFailed: Cannot launch daemon, file not found or permissions invalid   (nm-applet:2716): nm-applet-WARNING **: Could not find ShellVersion property on org.gnome.Shell after 5 tries   (nm-applet:2716): nm-applet-WARNING **: Failed to register as an agent: (2) The name org.freedesktop.NetworkManager was not provided by any .service files    Is there a patch I can download through windows and send through to my ubuntu, or is it a case of having to reload everything? I tried running two versions back but still no internet access. How to create script with auto-complete? When I use program like svn and I type in Gnome Terminal:  svn upd   and hit Tab it's autocompleted to:  svn update   Is it possible to do something like that in my custom bash script? How to clone ArrayList and also clone its contents? How can I clone an ArrayList and also clone its items in Java?  For example I have:  ArrayList&lt;Dog&gt; dogs = getDogs(); ArrayList&lt;Dog&gt; clonedList = ....something to do with dogs....   And I would expect that objects in clonedList are not the same as in dogs list. Proving the snake lemma without a diagram chase How do you get the current time in milliseconds (long), in VB.Net? How to run firefox and firefox ESR simultaneously How to create an Atlas based on point attributes? Essentially I am wanting to produce an atlas based on a categorical field in a point layer.   i.e. I have a point layer of childcare providers with the categorical field "Provision". I've categorized each feature in this field with "After School Club" , "Breakfast Club" etc, and I now want to produce a set of maps that iterate through each category and show only the points for each. One map of after school clubs, one map of breakfast clubs etc. The extents might be subtly different.  I could do it one by one but it seems like there should be a way to produce an atlas based on the extents of each category? (I do feel i'm missing something obvious :) )   Or alternatively is there a way of automating the creation of a polygon layer and using that as a hidden coverage for the atlas?  EDIT: I've made a little progress with this  - you can use rule based styling to switch on and off features relevant to the current atlas coverage feature.  it actually works fine if all you want to do is show a different set of points. I'm now looking at tying that back to a color scheme and reactive legend. Create an Application without a Window How would you program a C/C++ application that could run without opening a window or console? Show that SO(n) is a normal subgroup of O(n).  A normal subgroup is a subgroup which is invariant under conjugation by members of the group of which it is a part. SO(n) is the set of orthogonal matrices of determinant 1. O(n) is the set of real matrices whose inverses equal their transposes (orthogonal matrices). I'm simply bad at writing proofs. Please help? Does the  tag position in HTML affects performance of the webpage? WinError 32 error when trying to delete shapefiles with QGIS python When needing to ask a professor about something important and potentially delicate, what is an appropriate way to phrase the question or write the email?  Examples include:   Requesting a recommendation letter Asking for exceptions to policy (e.g., ignoring a course prerequisite, rescheduling an exam) Asking if you can do research with them, join a group, get into a program Scheduling a meeting, exam, or defense Letting them know about a change of plans Letting them know about a life event affecting your work or studies (e.g., wedding, funeral, sickness, vacation) What are the pros and cons of an articulated display? Embedding $S_n$ into $A_{n+2}$ I am trying to prove that for all $n$, $S_n$ is isomorphic to a subgroup of $A_{n+2}$.  Say $S_n$ acts on $\{\alpha_1,...,\alpha_n\}$ and $A_{n+2}$ acts on $\{\alpha_1,...,\alpha_n,\alpha_{n+1},\alpha_{n+2}\}$.  Let $\sigma \in S_n$ and let $\phi: S_n \to A_{n+2}$ be given by $\phi(\sigma)=\sigma$ if $\sigma$ is an even permutation, and $\phi(\sigma)=\sigma(\alpha_{n+1}\alpha_{n+2})$ if $\sigma$ is an odd permutation.  This way $\phi(\sigma) \in A_{n+2}$.  Now, let $\sigma, \rho \in S_n$.  Then $\phi(\sigma \rho)=\sigma \rho (\alpha_{n+1}\alpha_{n+2})$.  Also, $\phi(\sigma)\phi(\rho)=\sigma(\alpha_{n+1}\alpha_{n+2})\rho(\alpha_{n+1}\alpha_{n+2})=\sigma\rho$.  So, $\phi(\sigma \rho)$ does not seem to equal $\phi(\sigma)\phi(\rho)$.  But the idea is that we want $\phi(S_n) \cong S_n$, and $(\alpha_{n+1}\alpha_{n+2})$ does not permute any members of $\{\alpha_1,...,\alpha_n\}$, so $\phi(\sigma \rho)$ and $\phi(\sigma)\phi(\rho)$ are equal as permutations on this (sub)set.  This feels a little subtle to me and I'm not sure if my idea is valid or not.  If it is not, can this proof still be saved?  I appreciate any thoughts on this.  Thanks. A not free $\mathbb{Z}$-module From  I see that $\mathbb{Z}^{\mathbb{N}}$ is not a free abelian group. Someone can explain me why?  Thanks a lot! What should I do if I want to be able to run a given program regardless of my current directory? Should I create a symbolic link to the program in the /bin folder?