I did a question in which, the intensity of the incident radiation on a metal surface was kept constant but the wavelength of the photons has been reduced. The question inquired what will be the effect on the maximum photoelectric current? The initial wavelength was smaller than threshold wavelength of the metal surface.  My thinking was since the intensity remains constant, thus the number of photons emitted from the source remains constant and thus the number of electrons emitted from the metal surface. And since number of electrons per unit time isn't changed, the current will remain the same.  However, the answer key stated "Fewer photons (per unit time) so (maximum) current is smaller"   How does decreasing wavelength (equivalent to increasing the energy of photons) result in a fewer photon emission?
We all know that the amount of current flowing b/w the plates is independent of the frequency. If I were to ask why doesn't it depend then you'd probably say that it depends on the number of electrons rather than the frequency or you might show me a current vs frequency graph.  But here is my theoretical argument. Electric current is defined as the amount of charge flowing through a point/space/wire per unit time. Let I be current due to photo electrons ejected by photons of some frequency. Now if I would increase the frequency, the kinetic energy of the ejected electron would increases, therefore it will move faster and therefore contribute more current (charge will through the same point many times per unit time) . Thereby, giving a net current greater than I.  What is wrong with my argument?  After thinking a lot, I came up with a possible reason. However fast the electrons may move, but when they hit the metal plate, they would lose their velocity and start moving in drift velocity. Now there is a problem with this argument. If this were to be true then I should expect to see a big chunk of extra electrons getting stuck at the anode.  If my reasoning was correct, then why can't I see a big charge buildup at the anode.
I want to find out the number of possible combinations of $x$ numbers that sum to $y$. For example, I want to calculate all combination of 5 numbers, which their sum equals to 10.  An asymptotic approixmation is also useful. This question seems to be very close to number partitioning, with the difference that a number can be 0. See:    All possible partitions for sum 10 and 3 positions that can be zero, are 63 possiblities: (numbers shown as 3 digits)  019 028 037 046 055 064 073 082 091 109 118 127 136 145 154 163 172 181 190 208 217 226 235 244 253 262 271 280 307 316 325 334 343 352 361 370 406 415 424 433 442 451 460 505 514 523 532 541 550 604 613 622 631 640 703 712 721 730 802 811 820 901 910 Yesterday, Asaf Karagila's  sparked an extensive discussion on ways of proving that all countable ordinals are embeddable in $\Bbb Q$, and whether particular solutions to this use the Axiom of Choice.  Since the arguments used to prove this can be shady on their use of Choice when formulated tersely, fully fleshed out answers are appreciated.  To be concrete, this question asks for proofs of the following fact:     All countable ordinals $\alpha &lt; \omega_1$ are order-embeddable in the rationals $\Bbb Q$.   Especially answers avoiding the Axiom of Choice are appreciated.    Of relevance and related interest is  (but it's not a duplicate, since that question asks for explicit embeddings). $A \subseteq \mathcal{R}(N)$ and given that (by inductive definition):   $N ∈ S$. If $a \in R$, then $R \setminus \{a\} \in A$.    I need to prove that for each $A \in S$, $N\setminus A$ is finite. How can I prove this formally? If $\gcd(a,b)=1$, then there exists integers $x$ and $y$ such that $xa + yb = 1$ Did not find this from this website...  If $$ \gcd(a,b)=1,$$ then there exists integers $x$ and $y$ such that $$xa+yb=1.$$  Now, the tip is to use particular corollary, that states:  The class $[m]_{n}$ generates $\mathbb{Z}/n\mathbb{Z}\Leftrightarrow \gcd(m,n)=1.$  I am totally lost with the corollary.  Let's assume that $\gcd(m,n)=1$. Then, $[m]_{n}$ generates $\mathbb{Z}/n\mathbb{Z}$.  OK! Then what?  There is also follow up, where I have to prove the converse. I am familiar with Bezout's lemma. Divisibility tests and remainder mod $9,11,99,101,999,1001\,$ (casting out nines and elevens) Now I have proved the following two problems:      (1) Prove that a number and the sum of its digits have the same remainder upon division by 9.    (2) Given an integer, consider the difference between the sum of the digits in odd positions (counting from the right) and those in even positions. Show that the difference has the same remainder as the number itself when divided by 11.    Then, I need help on the following problem:      Partition the digits of a number into groups of two and three, respectively, starting from the right. Treat these as two- and three-digit numbers, respectively, and proceed similarly as in the two problems above. What divisibility rules arise?    In fact, I did not quite get what this problem asks for and not clear about this process. Could anyone give me some hints on this, please?  Thanks in advance. Comparing $\pi^e$ and $e^\pi$ without calculating them Is the word "management" singular or plural? Possible Duplicate:          Which one of the following is correct?     Management gets its ideas from its employees.   Management gets their ideas from their employees. The tennis statistics at the end of a set always show the number of winners and unforced errors of the players. But when does a point count as a winner and when as unforced error? Is there a proof that $\pi$ is an irrational number? Most math texts claim that $\pi$ is an irrational number. However, I'm having a little bit of trouble understanding that.  Since nobody has calculated all of the digits of $\pi$, how can we know that either:   one of the digits repeats (as in $\frac{10}{3}$) the number eventually terminates     Note: Please be very descriptive in your answers... I don't have anything beyond high school math. Is it possible to make abstract classes in Python? Mutineers force captain to record instructions to spaceship's computer but he leaves out "please" The crew mutinies on a spaceship whose captain controls it with verbal orders. They test whether they can control the ship with recordings of the captain's voice with an order to increase orbital speed (currently orbiting a planet). It works, so they force the captain to record all the possible orders they may need, and execute him. Only then do they realize that the ship obeys only orders couched in polite language, and only the test recording was like this, but the other recordings are not. They will die once the ship's faster orbit somehow causes it to run out of fuel, or something like that. I seem to remember the ship's &quot;computer&quot; following the captain around on robotic legs. I read the story circa 1980, but it might have been published much earlier. How can you move a document with its version history to a new library? Here's the scenario:  2 document libraries Both contain multiple documents The documents have multiple versions  When I copy a document from library A to Library B using the Content and Structure tool from Site Settings, my versions do not carry over. I'm trying to merge the two document libraries into one, but I want to retain the versions. Do you know of a way to complete this without third party tools or custom code? I've heard suggestions of using Explorer View copy and paste, SharePoint Designer and List Templates, but I'm not sure any of those will carry version info. Modern solution For modern SharePoint experiences, use Move To. Update 4/24/2018: There's a new solution in Office 365. You can now select a file or group of files in the modern experience in OneDrive or SharePoint and select Move to. A file or group of files moved this way will retain version history. Update 6/6/2021: As @KJH mentioned in a comment, you may not see the modern experience unless you . Also, there's more detail now in the Microsoft article . Determinant of an $n\times n$ complex matrix as an $2n\times 2n$ real determinant If $A$ is an $n\times n$ complex matrix. Is it possible to write $\vert \det A\vert^2$ as a $2n\times 2n$ matrix with blocks containing the real and imaginary parts of $A$?  I remember seeing such a formula, but can not remember where. Any details, (and possibly references) for such a result would be greatly appreciated. How to render from Eevee in Blender 2.8? I have the Blender 2.8 version from the 21st Sep 2018 I was looking forward to render a test sequence but cannot find a render button anywhere? Does anyone know where to find it? 'was' versus 'had been' When I asked the driver/ to come with me to the temple/ he had been reluctant./ No error.   I think instead of 'had been', there should be 'was'. Even the answer key points that the error is in the 'he had been reluctant' part. But I am not sure why exactly is 'had been' wrong.  If we replace the first part with 'when I had asked the driver', would that make 'had been' in the third part correct? SSH to open GUI on target machine? How to convert physical Ubuntu operating system into a virtual machine? A while ago I turned my PC into dual boot with Windows and Ubuntu. But my experience is, that I rarely boot into Ubuntu, so I wanted to make it available as virtual machine in Windows rather than as a second OS. Can you provide me some information which is the tool of my choice and how I can achieve this migration? I already have VMWare Player installed. I want to upgrade my disk from MBR to GPT, and I tried using Windows' MBR2GPT.EXE tool to do the job. I used Windows' DISKPART tool to identify the disk I want to convert. However, this happened:  C:\WINDOWS\system32&gt;MBR2GPT.EXE /convert /disk:0 /allowfullos  MBR2GPT will now attempt to convert disk 0. If conversion is successful the disk can only be booted in GPT mode. These changes cannot be undone!  MBR2GPT: Attempting to convert disk 0 MBR2GPT: Retrieving layout of disk MBR2GPT: Validating layout, disk sector size is: 512 bytes Disk layout validation failed for disk 0 MBR2GPT: Conversion failed   and the conversion failed. Using Diskpart again, I get the following output:  DISKPART&gt; list disk    Disk ###  Status         Size     Free     Dyn  Gpt   --------  -------------  -------  -------  ---  --- * Disk 0    Online          465 GB      0 B   Disk 1    Online         3841 MB   960 KB  DISKPART&gt; select disk 0  Disk 0 is now the selected disk.  DISKPART&gt; list partition    Partition ###  Type              Size     Offset   -------------  ----------------  -------  -------   Partition 1    Primary            100 MB  1024 KB   Partition 2    Primary            464 GB   101 MB   Partition 3    Recovery           813 MB   464 GB   Partition 4    Recovery           511 MB   465 GB   Looking at the partitions on disk 0, there are 2 primary partitions and 2 hidden ones, I read  that the partitions might have something to do with the conversion failing, so I believe this is the culprit. If anyone could offer help converting my disk, that would be greatly appreciated. (Re?)Install Ubuntu on a Dell laptop that had Ubuntu preinstalled Alice has a secp256k1 key pair that she used some time ago when she communicated with Bob. Bob can no longer user secp256k1 but he only uses ed25519 instead.  Is there a secure algorithm that Bob can use to derive an ed25519 pubkey from original Alice's secp256k1 pub key and also Alice can derive the matching ed25519 private key from her original secp256k1 private key such that they can communicate securely via ed25519 encrypted messages?  Thanks!