The energy required to remove an electron from the surface of a metal is less than that required to remove an electron from a free atom. Why?The electron is bound to the nucleus in an atom by electrostatic forces. How is an electron 'free' on a metal surface?
In a particular textbook, the work function of a metal (in the context of the photoelectric effect) is defined as:     the minimum amount of energy necessary to remove a free electron from the surface of the metal   This sounds similar to ionisation energy, which is:     the amount of energy required to remove an electron from an atom or molecule in the gaseous state   These two energies are generally different. For instance, Copper has a work function of about 4.7eV but has a higher ionisation energy of about 746kJ mol-1 or 7.7eV.  I've sort of figured it's because the work function deals with free electrons whilst ionisation is done with a valence electron still bound within the atom. Is the difference due to the energy required to overcome the attraction of the positive nucleus?
I have made a raster elevation map of Greenland, and have information of the region, cities and more as vectors. The information is not in the same place as my elevation map.  I have selected EPSG:5938 on the bottom right in QGIS and on my informations and elevation map I have set the CRS to the same like the picture    How do I get it all on the same position? How can you prove that the normal equations: $(X^TX)\beta = X^TY$ have one or more solutions without the assumption that X is invertible?  My only guess is that it has something to do with generalized inverse, but I am totally lost. Determine number of pages in a PDF file Can multiple different HTML elements have the same ID if they're different elements? What is the difference between encrypting some data vs signing some data (using RSA)?    Does it simply reverse the role of the public-private keys?    For example, I want to use my private key to generate messages so only I can possibly be the sender.  I want my public key to be used to read the messages and I do not care who reads them.  I want to be able to encrypt certain information and use it as a product-key for my software.  I only care that I am the only one who can generate these.  I would like to include my public key in my software to decrypt/read the signature of the key.  I do not care who can read the data in the key, I only care that I am the only verifiable one who can generate them.  Is signing useful in this scenario? Can I run the python interpreter without generating the compiled .pyc files? How do I audit my reputation? If I am concerned that my reputation score is incorrect, how can I audit it, or get a report of a detailed breakdown of my reputation? Let $f : U \to V$ and $g : V \to W$ be linear transformations on the vector spaces $U$, $V$, and $W$. Supposedly,  $$ \dim(\ker(g \circ f)) = \dim(\ker(f)) + \dim(\ker(g) \cap \operatorname{im}(f)). $$  How might I go about proving that?    (Attempt:) The $\dim(\ker(g)\cap\operatorname{im}(f))$ term suggests to me that I should define a vector space $V' = \ker(g) + \operatorname{im}(f)$ to invoke the theorem that  $$ \dim(V') = \dim(\ker(g)) + \dim(\operatorname{im}(f)) - \dim(\ker(g) \cap \operatorname{im}(f)), $$  but I don't really see where to go from there. I'm currently working on a scene containing 1000+ objects which all need to be set to a different draw type to save on computationally expenses in the viewport. But doing this for every object separately is really tedious. Therefor I'm wondering if there's a way to change the maximum draw type of multiple objects simultaneously. Preferably only the selected objects. Suspended user cannot award bounty I asked a question on Stack Overflow: . I want to award my bounty to  by user  However, my Stack Overflow account is suspended recently for 7 days, and the suspension still has 5 more days to end.And I know I can't vote, ask, answer or comment as pointed on  by  with the sentence below.  You will be unable to vote, ask, answer, or comment.  I couldn't find anything about not being able to accept an answer or award bounty so I tried to accept the mentioned answer above and award my bounty to it and I got a  Suspended users cannot vote  rejection which can be seen below with a screenshot.  I know this  If you do not award your bounty within 7 days, the highest voted answer created after the bounty started with at least 2 upvotes will be awarded half the bounty amount.  from . None of the answer given to my question is upvoted and the answer I mentioned is not the oldest one after the bounty started so it won't be awarded by community. What can I do? (except being a good guy and not get suspended :)) Substitute for onions and garlic Detecting absolute motion inside a box This is not a contradiction and I know it is impossible but still consider a thought experiment by me and point out if something is wrong. See the following picture and then the explanation follows.    Rest frames are easy to understand. They are just for clarification. Lets move on to the moving frames. The velocity of the box is $0.1\ c$. Now a photon is emitted (I am not taking a light ray to avoid complication in discussion). After emission the box also moves a certain distance ahead. So the photon takes more than one second to reach the wall. But even the source moves that much distance ahead. When the light is reflected back, the source and the wall again move forward as the box is moving. But after reflection the wall has no role to play. We are concerned about the source. The source moves a certain distance ahead and therefore light takes less than one second to reach back. But the difference of the first case and the second case is not the same. To explain, I will give some equations.  Moving frame 1:  Velocity of the box: $0.1\ c = 30,000km/s$  Time taken by light to reach the wall $=\frac{330,000\ \text{km}}{300,000\ \text{kms}^{-1}}= 1.1s$  Distance moved ahead by the box from original position: $30,000\ \text{km}$  Moving frame 2:  distance moved ahead by the box from original position  $&gt;30,000\ \text{km}$ as the box also moves ahead after reflection.  let $d$ be the distance moved ahead by the box after reflection.  Time taken by light to reach the source: $\frac{270,000\ \text{km}\ -\ d}{300,000\ \text{kms}^{-1}} &lt;0.9s$  Therefore we see that this could possibly determine the absolute motion.  So in total we see that the light will take lesser time to reach the source. Please correct me if I am wrong and give your opinion why is it so.  EDIT 2 for clarification  The box is the compartment in space in which you are moving and I am calculating the time the light takes to reach back the source. I am not even adding velocities. Please correct me and tell me where did I add velocities. For clarification just let me give a simple example. Suppose person A is standing still and B is running towards a light source. Obviously he will see the light before person A even though the speed would be the same. So, what I am doing over here is not increasing the speed of light, but instead decreasing the distance to be covered by it. Cron Job not working in plugin I have written a plugin that will convert posts to excel format and then email the .xls to an email id. I can make it work with when function is declared in functions.php but does not work with function defined in plugin file.   if ( ! wp_next_scheduled( 'xls_func_hook1' ) ) {   wp_schedule_event( time(), 'hourly', 'xls_func_hook1' ); }  add_action( 'xls_func_hook1', 'sendxls1' ); //senxls1 is a function in functions.php if ( ! wp_next_scheduled( 'xls_func_hook2' ) ) {    wp_schedule_event( time(), 'hourly', 'xls_func_hook2' ); } add_action( 'xls_func_hook2', 'export2excel' );   The full code is at When I receive a message on an SE post, I get a notification like this:    If I double tap this notification, the SE application opens, but my feed is empty approximately half the time. It looks like this:    If I refresh the feed (slide from the top), the feed does refresh and shows the new notification.   The notification, above, leads to  comment.  I haven't figured out the pattern yet, but this occurs roughly half the time I open a notification. It's occurred for chat messages, comments and answers - but not consistently. I have received notifications for the same post (for example, the two comments after the one linked above) that do not show an empty feed. But, a chat message barely 10 minutes later will show the empty feed again.  I am utilizing the beta app - version 1.0.72 on Android 5.0.1. How to skip kernel update? Definition respective derivation of angular momentum formula I am reading An Introduction to Mechanics by Kleppner and Kolenkow (2014). On page 241 is the definition of the :      Here is the formal definition of the angular momentum $\vec{L}$ of a particle that has momentum $\vec{p}$ and is at position $\vec{r}$ with respect to a given coordinate system: $$\vec{L}=\vec{r} \times \vec{p}$$   In the book there is no explanation why this formula should be true. From this equation the formulas for torque and moment of inertia are derived.   My question is: Why is the formula above correct? Why isn't the formula for angular momentum something completely different, like $\vec{L}=\sqrt{(\vec{r} \times \vec{p})2\pi M}$? Is the formula for angular momentum just a mere definition and if not, how to derive it? How did people come across that particular formula? Shortest code to calculate list min/max in .NET I'd like something like  int minIndex = list.FindMin(delegate (MyClass a, MyClass b) {returns a.CompareTo(b);});   Is there a builtin way to do this in .NET? Are other players able to see you on their map in Pokemon Go? I am concerned that if I use the game, stalkers and other such people would be able to find me. I have searched for an answer for this question on other forums, but have yet to find the answer. Why does water pouring from a glass sometimes travel down the side of the glass? If you have a glass of water, say, three quarters full and you pour it at an angle of say, $45^{\circ}$ with respect to the the table, the water comes out of the glass and goes directly down towards the floor.  However, when the glass is more full, or even three quarters full and the 'angle of pouring' is far less with respect the table, when the water comes out of the glass, rather than going straight down it kind of stays stuck to the glass and travels down the outside of it.  Why does this happen? (I'm sure many of you have observed it yourself by accident and ended up making a mess). every rank 2 oriented matroid is realizable