At what element do we hit a wall because of the electrons relativistic speed?  i.e. the speed of the outer shells can go no faster?
With the confirmation that elements 113, 115, 117, and 118 are indeed fundamental elements that are now to be named on the periodic table, the next question is: what is the highest atomic number possible for an element? Feynman had a go at this years ago, and he derived (according to my limited understanding) that above element-137 (informally denoted 'Feynmanium') the electrons in the nearest orbit about the nucleus would be traveling at a velocity greater than the speed of light. (Note I am considering the Bohr model of the atom in this question.) I wished to demonstrate to my friends why this is and I came up with the following explanation.  According to Bohr's quantum condition, the angular momentum of an electron about the nucleus is given by $$ L=m_evr_n=n\hslash \implies r_n=\frac{n\hslash}{m_ev},$$ where $m_e$ is the mass of the electron, $v$ its velocity, $n$ an integer, and $r_n$ the radius of the $n$th possible orbit. Because we are concerned with the nearest orbit to the nucleus, $n=1$; and thus $$r=\frac{\hslash}{m_ev}.$$   Now, according to Coulomb's law, if the electron orbits about the nucleus the centripetal motion can be described by $$\frac{Ze^2}{4\pi\epsilon_or}=m_ev^2, $$ where $Z$ denotes the number of protons in the nucleus (the atomic number), and $e$ the elementary charge. Solving for $Z$ and substituting in $r$ from above yields $$Z=\frac{4\pi\epsilon_o \hslash v}{e^2}. $$ But what is $v$? Well, the maximum velocity an electron could ever have is the speed of light, and we wish to find the atomic number associated with an orbiting electron traveling at this speed, so we set $v=c$ and obtain our final result of $$Z=\frac{4\pi\epsilon_o\hslash c}{e^2}\approx 137.521,$$ which implies that for $Z&gt;137$, the electrons at a position of $n=1$ in the Bohr model would have a velocity $&gt;c$; and thus the highest atomic number achievable on the periodic table is 137.  Again, I just want to make sure this is a correct method for deriving element-137 before presenting. Perhaps one could explain how relativity plays a role here. I know Feynman used the Dirac equation to get this result...so could anyone (subsequently of course) expatiate on this in a simplistic manner? Thanks!
I have recently started using blender and one of the models I'm working on has dark shadows along edges. I started this model from scratch. I can't remember them being there when I first started the model, but I had trouble joining areas together and think I've pressed something I shouldn't have. However, there are so many options I'm not sure what I did.  Here is an image of what I mean   The one on the left has the shadow. As a test I started a new model, which is on the right in the image, and as you can see it doesn't have any shadows.  Also, occluded vertices partially show through the model. Occlusion doesn't work properly.   In orthogonal view small darkened triangles appear along the the edges.    I don't really want to start the model again from scratch so any ideas on how to remove this shadow would be great. Thanks. Is there any way of making a snow golem survive in hot biomes? Snow golems won't survive in the Nether (neither spawned in nor built ones). Is there a way to make a snow golem survive in the Nether and other hot biomes in vanilla Minecraft (i.e., without using mods)? Was Grand Moff Tarkin under Darth Vader's control? In A New Hope, we see Grand Moff Tarkin ordering Darth Vader around. Also, it was . It's uncertain whether he knew .  But considering that Darth Vader was a Sith Lord, and a Jedi before that, are we entirely sure he wasn't secretly controlling Tarkin through a Jedi Sith mind trick? What happens when yellow light is passed through a prism? What happens when secondary colors like yellow,green and magenta are passed through a prism? Will it split into its component colors(for example yellow split into green and red)?If yes why we are observing secondary colors in the visible spectrum obtained when white light(composite light) is passed through a prism? How to find and delete identical points? I recently performed  on a merged point feature class in ArcGIS 10.1.  I specified "1 meter" XY tolerance for the Integrate command.  The resulting point feature appears to be what I want except points that were integrated are now stacked on top of each other, which will be problematic in future processing steps.  The attributes for my dataset consist of an OID, Shape, x, y, z.  Where x and y = UTM coordinates and z = buffer distance.  The command  does not appear to work for my dataset (i.e based on Fields: OID, Shape, x, y, z and XY tolerance = 1m) as the output still has stacked points.  I am also working with big data--the integrate output has 37 million points.    There is a related thread, titled , although I would like to open the question up to python solutions too.  What is the best way to find and delete (spatially) duplicate points?  Is there a better solution to integrating such that the output does not contain overlapping points? Do I need to pay in full for hostel reservation to show proof of accommodation for a Schengen visa? I am applying for a Schengen visa to travel to Germany and one of the requirements is showing proof of accommodation. I booked all my hostels via hostelworld.com, but only paid the non-refundable deposit (a couple of dollars for each place) instead of the entire amount. I intend to pay the rest of it on arrival at the hostel (or cancel it and go CouchSurfing, thus saving money).  But for the visa application, will the non-refundable deposit be enough to show proof of accommodation?  The reason I ask is, I emailed one of the hostels requesting a document showing my name and accommodation confirmation, and they replied saying they could only give me such a document once I pay in FULL.  Is this how I'm supposed to book for all places?  Have I been doing it wrong all this while (by only paying the tiny non-refundable deposit instead of full hostel fare)? There is a restriction on setting your birthday:     Oops! There was a problem updating your profile:   - Birthday must be after 1920/01/01   I realize the number of 90 year old users is small, but shouldn't the restriction be a bit more relaxed, such as larger than any ?  Either 120 or 150 seems appropriate.  For example, my grandfather turns 90 next year (and just barely misses the current cutoff), but I can't imagine he's the only one around that age who is computer literate and still active enough to be interested in (the increasingly broad range of) SE sites.  I don't think he has contributed yet (mostly because of the comment restriction, I'd see him commenting before asking or answering), but I have emailed him with links that I know he's read.  Incidentally, the error message is wrong: birthday must be after 1919/12/31 and using the next day is accepted. Generator expressions vs. list comprehensions When should you use generator expressions and when should you use list comprehensions in Python?  # Generator expression (x*2 for x in range(256))  # List comprehension [x*2 for x in range(256)] US Election results 2016: What went wrong with prediction models? First it was , now the US election. Many model predictions were off by a wide margin, and are there lessons to be learned here? As late as 4 pm PST yesterday, the betting markets were still favoring Hillary 4 to 1.  I take it that the betting markets, with real money on the line, should act as an ensemble of all the available prediction models out there. So it's not far-fetched to say these models didn't do a very good job.  I saw one explanation was voters were unwilling to identify themselves as Trump supporters. How could a model incorporate effects like that?  One macro explanation I read is the rise of . The question then is how could a statistical model capture a macro trend like that?  Are these prediction models out there putting too much weight on data from polls and sentiment, not enough from where the country is standing in a 100 year view? I am quoting a friend's comments. What are the use cases of SO_REUSEADDR? I have used SO_REUSEADDR to have my server which got terminated to restart with out complaining that the socket is already is in use. I was wondering if there are other uses of SO_REUSEADDR? Have anyone used the socket option for other than the said purpose? Why are so many forces explainable using inverse squares when space is three dimensional? Several lines of formulas to the left of one curly brace pointing to equation number How to make several lines of equations under one curly brace from the left side, such that it point to a reference number.  Now I do something like this:  \begin{align} \left. \begin{array}{ll} a = b + c \\ &amp; \dots  \\ a = b + c \\ &amp; \dots  \\ a = b + c  \end{array} \right\} \label{formulas}\\ \end{align}   But equation number appears in the bottom of curly brace. Is my US visa still valid after change in name? I'm a Malawian national and I got US Visa years back.  Recently, due to some reasons, I had to get my first name partially changed on my passport. I have got an affidavit certificate stating the reason and proof.  Since the visa on my old passport has still not expired, but there is a difference in first name, will I face any problem? Why is the voltage across a capacitor and the current across an inductor continuous? How to test if a string is basically an integer in quotes using Ruby Find and Replace Inside a Text File from a Bash Command What is the correct way to completely remove an application? I've searched the net for such information and found different command lines, like these ones:  sudo apt-get remove application sudo apt-get remove application*  sudo apt-get remove --purge application sudo apt-get remove --purge application*  sudo apt-get purge application sudo apt-get purge application*   So, what is the correct way? Is it necessary to use that "*"?  After that, I also found these commands:  sudo updatedb sudo locate application sudo rm -rf (file/folder name) What is a NullPointerException, and how do I fix it? What are Null Pointer Exceptions (java.lang.NullPointerException) and what causes them?  What methods/tools can be used to determine the cause so that you stop the exception from causing the program to terminate prematurely? I was making this recipe: , which was from the old Lincoln Del, one of my mom's favourite places. I mistakenly doubled the sugar, putting in 1/2 a cup instead of a 1/4 of a cup. Given the 2/3 of a cup ketchup, which was Heinz, the soup turned out way, way too sweet.   Is there any way I can rescue this? Short story about humans serving as hosts to the larval stage of insects I read this story in a sci-fi paperback magazine probably in the 1970s or 1980s, but it might have been published much earlier.  It begins with a conversation between two young men (brothers?), the older of whom, it eventually transpires, has taken the place of the younger in serving as a host to insect-type creatures.  The insect-types are the main form of life on the planet, and use the human interlopers/colonizers as hosts for the larval stages of their    young. Must have pre-dated the &quot;Alien&quot; movies because when I read it the idea of humans serving as larval hosts was new to me. Don't remember how the story ends -- whether the emergence of the larva kills the human host.