A problem in Bohr's day was understanding why an orbiting electron does not continuously radiate an EM field. An orbiting electron is a moving charge and according to Maxwell, this should generate an electric and magnetic field. Bohr said that photons (packets of EM energy) are only emitted when an electron jumps from a high quantum state to a lower one. Does that mean that an electron in a stable atom really isnt moving? Conversely, does Bohr's model mean that all motion requires energy transitions from one qunatum sate to another?
I'm having trouble understanding the simple "planetary" model of the atom that I'm being taught in my basic chemistry course.   In particular,    I can't see how a negatively charged electron can stay in "orbit" around a positively charged nucleus. Even if the electron actually orbits the nucleus, wouldn't that orbit eventually decay?  I can't reconcile the rapidly moving electrons required by the planetary model with the way atoms are described as forming bonds. If electrons are zooming around in orbits, how do they suddenly "stop" to form bonds.     I understand that certain aspects of quantum mechanics  to address these problems, and that there are  of atoms. My question here is whether the planetary model itself addresses these concerns in some way (that I'm missing) and whether I'm right to be uncomfortable with it.
Multiple addresses in JSON-LD Schema.org What is the variance of the weighted mixture of two gaussians? Say I have two normal distributions A and B with means $\mu_A$ and $\mu_B$ and variances $\sigma_A$ and $\sigma_B$. I want to take a weighted mixture of these two distributions using weights $p$ and $q$ where $0\le p \le 1$ and $q = 1-p$. I know that the mean of this mixture would be $\mu_{AB} = (p\times\mu_A) + (q\times\mu_B)$.  What would the variance be?    A concrete example would be if I knew the parameters for the distribution of male and female height. If I had a room of people that was 60% male, I could produce the expected mean height for the whole room, but what about the variance? How did Enrico Fermi calculate the classical Fermi Problem? From Wikipedia: Fermi was known for his ability to make good approximate calculations with little or no actual data, hence the name. One example is his estimate of the strength of the atomic bomb detonated at the Trinity test, based on the distance travelled by pieces of paper dropped from his hand during the blast. Fermi's estimate of 10 kilotons of TNT was remarkably close to the now-accepted value of around 20 kilotons, a difference of less than one order of magnitude.  I have not been able to find any references explaining how he made this calculation. Please provide a reference or an example calculation.  See also: I am being driven crazy by the fact that my media keys aren't working for iTunes. Such a pain! How can I fix this? I've tried the whole Chrome Extensions thing, that being I deleted all my extensions. Still, nothing has fixed this. Thanks to all who reply! This is on Stack Overflow. On Meta I'm able to see what the tags are on the right side of the screen. In fact, I think yesterday or some point earlier today I saw tags on the right side of the screen (I can't screenshot or remember correctly).  It's right above the asked and active heading.  I know this is minor but what happened to it? It might be useful for browsing instead of having to look at the bottom of the question post.    Found an image on Google and it shows the tags on the right side of the screen: List all my drafts In GMAIL you can list all your boss-tell-off and wife-cuss-out emails by clicking Drafts    I'd like to see my started-but-never-finished responses, possibly between x Answers and y Votes in /&lt;&lt;user&gt;&gt;/Stats/? Spyder - touchpad scroll does not work I use the scroll function with my mouse and it works fine. But either in script, or in terminal sections of Spyder, I can't use the touchpad for scrolling. I do not experience any problems with my touchpad in other programs like Word, Chrome etc. Is there any option for this in Spyder, specific for touchpad?  I am using Lenovo Legion Y520, Windows 10. Why does getopts only work the first time? Can't do comparison on PageReference In my page constructor I call a method isFirstPageLoaded, to  check if the loaded page is the first page of the wizard.   private final PageReference FIRSTPAGE = Page.Maintenance_Lock_1;   private void isFirstPageLoaded() {          if(ApexPages.currentPage()!=this.FIRSTPAGE) {              throw new MaintenanceLockException(this.FIRSTPAGE + ' --- ' + ApexPages.currentPage());          }      }   The problem is: Even if I open the first page of the wizard, the exception is thrown. How can I compare two PageReferences? I would like to avoid to parse the URLs and remove parameters etc... Kind of a strange question, but say something has spoiled, i.e. smells bad, tastes bad, etc.  Will it actually always make you sick? Like for instance spoiled dressing, let's say it tastes sour, smells nasty and you eat it, will it make you sick?  If so what actually makes you sick? The toxins/bacteria? or it just being unappetizing?  I ask because I tried a TINY bit of ranch and while it tasted mostly fine (it was a bit tangy) it smelled quite tangy but looked fine. I also saw . Does infinity exist in physical systems? Why does Worf want O'Brien to go to Minsk? I've just watched the last 20 minutes of an episode of Deep Space 9, and towards the end Worf is very insistent that O'Brien and his wife move to Minsk. Is there any in or out of universe reason for this? Can a lingering injury that requires "magical healing of 6th level or higher" be healed by an upcast lower-level spell? The  table in the DMG (p. 272) contains some wounds that can only be fixed by powerful healing magic, for instance:     Horrible Scar. You are disfigured to the extent that the wound cannot be easily concealed. You have disadvantage on Charisma (Persuasion) checks and advantage on Charisma (Intimidation) checks. Magical healing of 6th level or higher, such as heal and regenerate, removes the injury.   Can the necessary magical healing described here be a lower-level spell (such as cure wounds) that is upcast to 6th level? Or must it be a healing spell that is already 6th level or above before upcasting? Which features of a wizard's familiar, if any, are considered magical? The  spell has a duration of instantaneous, which implies that the familiar itself is not an ongoing magical effect. However, the spell provides a number of ongoing features that are definitely supernatural:    The familiar disappears when it drops to 0 HP. The wizard can temporarily or permanently dismiss the familiar. The wizard can communicate with the familiar telepathically. The wizard can observe through the familiar's eyes and ears. The familiar can deliver touch spells on behalf of the wizard.   Which of these features are considered magical? For example, would any of them show up to a detect magic spell or be suppressed by an antimagic field? In addition, is my assumption above correct that the familiar itself is not considered magical? I'm thinking that one way Jeff and the Stack Overflow team could squeeze some extra money out of this site would be to automatically convert all Amazon links posted here into affiliate links, e.g. Stick "tag=codinghorror-20" (or more likely a new site-specific tag) onto every Amazon link. This would bring in some additional revenue every time someone purchased a book via a link on this site.   They could do similar things with other links as well. Amazon's simply the most obvious choice.  So my question is, would anyone have a problem with this?  I know I wouldn't mind, but I don't know how other people would react.  What does everyone think? Is this a horrible idea, a great idea, a waste of time? How to make a logo where a letter is made of particles of varying sizes? How can I make a logo in Adobe Illustrator like the AntiParticle logo below, from ?   It is a large number circles of different, varying sizes, which form the shape of a text character. Self-Studying Measure Theory and Integration As the title says, I'm interested in reading about measure theory and integration theory on my own time, and was hoping for book recommendations, prerequisites, and things like that.  As for my background, I've taken introductory analysis, where we covered the "typical" subjects up until some theorems about differentiable functions.  I'm taking intermediate real analysis now; we talked about metric spaces in general for a while, but lately we've focused solely on $\mathbb{R}^n$. Now we're working towards a proof of the implicit function theorem in $\mathbb{R}^n$.  I haven't learned any of the theory behind Riemann integration, unfortunately. Is it important to be familiar with this first? Can we please move the  "Start a bounty" link to be in the same location as all of the other action buttons? It makes no sense to me for this to be buried after the comments - It's an action on the Question. It can be very difficult to locate, especially when your question gets .  I don't think this should be that difficult to implement - it's just moving the location of a design element. Can we please get this button moved? How to run sudo command with no password? How does the ubuntu user on the AWS images for Ubuntu Server 12.04 have passwordless sudo for all commands when there is no configuration for it in /etc/sudoers?  I'm using Ubuntu server 12.04 on Amazon. I want to add a new user that has the same behavior as the default Ubuntu user. Specifically I want passwordless sudo for this new user.   So I've added a new user and went to edit /etc/sudoers (using visudo of course). From reading that file it seemed like the default ubuntu user was getting it's passwordless sudo from being a member of the admin group. So I added my new user to that. Which didn't work. Then I tried adding the NOPASSWD directive to sudoers. Which also didn't work.   Anyway, now I'm just curious. How does the ubuntu user get passwordless privileges if they aren't defined in /etc/sudoers. What is the mechanism that allows this? For $u:\mathbb{R}\times [0,1]$ with boundary conditions $u(0,x)=\cos (2\pi x)$ and $u(t,0)=u(t,1)$.   Solve $u_t=u_{xx}+u_x$.  I had this on an exam and tried to write $u$ as a product of two single variate functions and convert to an ode using the usual methods but things got messy and I couldn't finish. I also tried to write $u$ as a Fourier series in $x$ with coefficients $a_k(t)$ depending on $t$, but this also didn't seem to yield anything.  Is there a more clever way to approach this, possibly with Fourier series? I heard from a friend there may be a Fourier transform method since the equation was "homogeneous in momentum space."   Thanks!