Periodic Definition and 437 Threads

The periodic table, also known as the periodic table of elements, is a tabular display of the chemical elements, which are arranged by atomic number, electron configuration, and recurring chemical properties. The structure of the table shows periodic trends. The seven rows of the table, called periods, generally have metals on the left and nonmetals on the right. The columns, called groups, contain elements with similar chemical behaviours. Six groups have accepted names as well as assigned numbers: for example, group 17 elements are the halogens; and group 18 are the noble gases. Also displayed are four simple rectangular areas or blocks associated with the filling of different atomic orbitals.
The elements from atomic numbers 1 (hydrogen) to 118 (oganesson) have all been discovered or synthesized, completing seven full rows of the periodic table. The first 94 elements, hydrogen to plutonium, all occur naturally, though some are found only in trace amounts and a few were discovered in nature only after having first been synthesized. Elements 95 to 118 have only been synthesized in laboratories, nuclear reactors, or nuclear explosions. The synthesis of elements having higher atomic numbers is currently being pursued: these elements would begin an eighth row, and theoretical work has been done to suggest possible candidates for this extension. Numerous synthetic radioisotopes of naturally occurring elements have also been produced in laboratories.
The organization of the periodic table can be used to derive relationships between the various element properties, and also to predict chemical properties and behaviours of undiscovered or newly synthesized elements. Russian chemist Dmitri Mendeleev published the first recognizable periodic table in 1869, developed mainly to illustrate periodic trends of the then-known elements. He also predicted some properties of unidentified elements that were expected to fill gaps within the table. Most of his forecasts soon proved to be correct, culminating with the discovery of gallium and germanium in 1875 and 1886 respectively, which corroborated his predictions. Mendeleev's idea has been slowly expanded and refined with the discovery or synthesis of further new elements and the development of new theoretical models to explain chemical behaviour. The modern periodic table now provides a useful framework for analyzing chemical reactions, and continues to be widely used in chemistry, nuclear physics and other sciences. Some discussion remains ongoing regarding the placement and categorisation of specific elements, the future extension and limits of the table, and whether there is an optimal form of the table.

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  1. jimmy neutron

    Numerically solutions with periodic boundary conditions

    Is anyone aware of how to numerically solve the (1D) SE with periodic boundary conditions?
  2. R

    Periodic Solution to Differential Equation

    For each epsilon greater than 0, show that the differential equation x'=x^2-1-cos(t)-epsilon has at least one periodic solution with 0 less than x(t) less than or equal to (2+epsilon)^1/2
  3. C

    Where should hydrogen be placed in the periodic table?

    Hi all, I was always of the belief that hydrogen did not belong to any group in the periodic table. After discussions, some say that a group 1 or 7 place might be more suitable. Any opinions would be welcomed hopefully from a physics point-of-view on this topic.Thanks in advance
  4. M

    MHB Why should the solution be periodic?

    Hey! :o The Laplace's equation with polar coordinates is: $$u_{rr}+\frac{1}{r} u_r +\frac{1}{r^2} u_{\theta \theta}=0$$ We suppose the boundary value problem with Dirichlet boundary conditions for the Laplace's equation on a disc with center the origin of axis and radius $a$...
  5. A

    Fourier transform of function times periodic function

    Suppose I have a function of the type: h(t) = g(t)f(t) where g(t) is a periodic function. Are there any nice properties relating to the Fourier transform of such a product? Edit: If not then what about if g(t) is taken as the complex exponential?
  6. J

    Spatial and temporal periods and periodic functions

    A periodic function is one that ##f(\theta) = f(\theta + nT)##, by definition. However, the argument ##\theta## can be function of space and time ( ##\theta(x, t)## ), so exist 2 lines of development, one spatial and other temporal: $$f(\theta) = f(kx + \varphi) = f(2 \pi \xi x + \varphi) =...
  7. M

    MHB Why is the right part of the Fourier series periodic with period L?

    Hey! :o The Fourier series of $f$ is $$f(x) \sim \frac{a_0}{2}+ \sum_{n=1}^{ \infty} {(a_n \cos{(\frac{2 n \pi x}{L})}+b_n \sin{(\frac{2 n \pi x}{L})})}$$ How do we know that the series of the right part of the above relation is periodic with period $L$?
  8. A

    MHB Periodic Function: Prove Smallest Positive Period

    One period of the function f(x)=\operatorname{tg}\frac{11x}{34}+\operatorname{ctg}\frac{13x}{54} is 918\pi. Please help me to prove that this is the smallest positive period. I can not use the most of trigonometric identities.
  9. J

    Representing a real periodic valued function with Fourier series

    Homework Statement Hey, the question i have been given reads: By a simple change of variables, show that if g(x) is a periodic real valued function with period L it can be represented as g(x)~ ∑∞n=-∞ An exp(-2\piinx/L) where the complex constants An are given by LAm =[L/2,-L/2]...
  10. C

    What Defines the Periodicity of a Driving Force in Harmonic Motion?

    Not a homework problem, just a question. What is a periodic driving force, specifically what is periodic about it? Is it the magnitude of the force that is periodic? Homework Statement Homework Equations The Attempt at a Solution
  11. B

    Can Multiple Periods Determine a Fundamental Period in Functions?

    Can a function have two periods? If so, which is the fundamental period? Consider the following function, $$ f : \mathbb{N} → \mathbb{R} $$, defined by f[n] = 1 if n is a multiple of 2 or 3, and 0 otherwise. Then it is clear that 2 and 3 are both periods of this function, since translation...
  12. Demon117

    Understanding Triply Periodic Surfaces: Translations and Invariance?

    So I understand that a surface is triply periodic when the surface is invariant under three tanslations in R^{3}. When looking at the primitive for example, how is that translation defined? Say that the primitive is a set defined by the equation cos(x)+cos(y)+cos(z)=0 My guess is that...
  13. M

    MHB Markov Chain - Is state 2 periodic?

    Hey! :o Given the Markov chain $\{X_n, n \geq 1\}$ and the following probability transition matrix: $\begin{pmatrix} 0 & 1/3 & 2/3\\ 1/4 & 3/4 & 0\\ 2/5 & 0 & 3/5 \end{pmatrix}$ All states communicate, so the chain is irreducible, isn't? Could you tell me if the state $2$ is periodic?
  14. J

    Representations of periodic functions

    Correct me if I'm wrong, but exist 3 forms for represent periodic functions, by sin/cos, by exp and by abs/arg. I know that given an expression like a cos(θ) + b sin(θ), I can to corvert it in A cos(θ - φ) or A sin(θ + ψ) through of the formulas: A² = a² + b² tan(φ) = b/a sin(φ) = b/A...
  15. H

    Strange reflectance from periodic structure

    Hi, last semester I did a project with two fellow students. We made a numerical model to calculate the reflectance from a periodic V-shaped structure of silicon similar to this: In the course of doing so, we came across something we could not explain. I have placed an image of it below...
  16. N

    Fourier series of a periodic function not starting at x=-L

    Homework Statement In "oppgave 4" http://www.math.ntnu.no/emner/TMA4120/2011h/xoppgaver/tma4120-2010h.pdf you have a periodic function which is NOT periodic from ##x=-L=-\pi## to ##x=L=\pi##, but at ##x=0## and ends at ##x=2 \pi=2L##. The formulas I have (like these...
  17. I

    How is the steady periodic oscillation used to solve problems?

    I have a homework problem that I need to use the steady periodic oscillation to solve, so instead of having help on the problem I'd rather just understand how they did it then apply it to my homework (I think that's alright?) I'm kind of wondering where my book gets this from...
  18. D

    Why this solution to the 3D periodic Navier-Stokes?

    Who can provide a physical understanding to this solution to the 3D periodic Navier-Stokes equation: http://purvanced.wordpress.com?
  19. H

    Electron collision and periodic crystal

    Ashcroft & Mermin, Solid State Physics, page 315: "According to the Bloch theory, an electron in a perfectly periodic arrays of ions experiences no collision at all". But how about the electron at the border of Brillouin zone? How does diffraction take place there?
  20. U

    Continuous Periodic Fourier Series - Coefficients

    Homework Statement In the dirac notation, inner product of <f|g> is given by ∫f(x)*g(x) dx. Why is there a 1/∏ attached to each coefficient an, which is simply the inner product of f and that particular basis vector: <cn|f>? Homework Equations The Attempt at a Solution
  21. Q

    Theory or Reality - Acid/base trends on the periodic table

    Homework Statement Number 12. Ignore the scribbling and the circled answers. http://i.minus.com/i17OAHo9PELaW.jpg Homework Equations The periodic table trend of acid/base behavior says that oxides of elements on the right of the periodic table will behave as acids in water. It...
  22. D

    Finding periodic best-fit equation for data set?

    Hello, I have a data set that follows an equation similar to sin(x)+x. Just from eyeballing the data, it seems like there should be a pretty simple trigonometric function A*sin(B*x)+C*x. I went to school for engineering so I have some basic/intermediate knowledge of mathematics but it's...
  23. A

    Complex Periodic Waves: Solving RLC Circuit

    Homework Statement A 100Ω resistor is connected in series with a 2 uF capacitor and a 20 mH inductor. The voltage 1 sin 5000t + 0.5 sin 1000t V is applied across the circuit. Determine: a) The effective (rms) voltage b) The effective (rms) current c) The true power d) The...
  24. Astronomer1

    Do Transition Metals Always Lose Electrons to Fill d-Subshells?

    1. Regarding: Transition metals of the Periodic Table 2. Here's my question: the D-Block transition metals will always lose e- (& never gain e-'s) to fully fill (or half-fill) their d-subshells, right? 3. Given what I learned about stable, fully-filled and half-filled subshells...
  25. R

    Classical mechanics ~ Potential energy and periodic movement

    Hey all, suppose there's a particle with Potential Energy : U(x) = A*[ x^(-2) - x^(-1) ] , where A is a constant. I'm supposed to find the energy required to make the particle go from periodic movement to unlimited movement. First thing I did was U '(x) = 0 to find the balance points, now...
  26. A

    Finding the Fourier Series of a periodic rectangular wave

    Homework Statement The problem/question is attached in the file called "homework". In the third signal (the peridic rectangular wave), I am requested (sub-question b) to find the Fourier series of the wave. Homework Equations The file called "solution" presents a detailed solution to the...
  27. A

    The webpage title could be: Solving for Power Factor in a Complex Circuit

    Homework Statement Could you please help me to start this question? Calculate the properties of complex periodic waves. A 100Ω resistor is connected in series with a 2 uF capacitor and a 20 mH inductor. The voltage 1 sin 5000t+0.5 sin 1000t V is applied across the circuit...
  28. M

    Weak periodic potential-degeneracy

    Hi; In chapter 9 of Solid state physics of Ashcroft&Mermin(Electrons in a weak periodic potential), there is a General Approch to the Schrodinger Equation when the Potential is Weak. i can't understand what is meant by the term DEGENERACY? or what does "nearly degenerate free electron...
  29. N

    Existence of non-orientable surface parametrized by periodic variables

    Hi! I was wondering: is it possible to have a non-orientable surface in 3D which is parametrized by u and v, with u and v periodic (i.e. is it possible to map the torus continuously into a non-orientable surface in 3D?) If so, does anyone have any explicit examples?
  30. J

    Periodic or not? Determine the wave function

    Homework Statement The following picture is supposedly periodic (or at least my teacher says so). Could anybody suggest where I begin in order to determine the wave function for this messy graph. Please see the attached for the graph.
  31. R

    How do I plot this periodic step function with GNUplot?

    \sum_{k=0}^{∞} (t-2k) [u(t-2k)-u(t-2(k+1))] = f(t) where u is the step function and the graph of this is supposed to be 45 degree lines repeating to infinity. Sort of like / / / / / / / / / ad infinitum. I took this equation out of this lecture note on page 10. Fig 5.4 is supposedly the graph...
  32. J

    Is f(x) = cos^2(x) + sin^2(x) a periodic function?

    Homework Statement Is f(x) = cos^2(x) + sin^2(x) a periodic function? Homework Equations sin^2(x) + cos^2(x) = 1 The Attempt at a Solution This question is just something that randomly came to my mind (not a homework problem). I know cos^2(x) and sin^2(x) are both periodic...
  33. H

    Expanding the periodic potentials

    Could one always write the periodic potentials in the form: v(r)=Ʃf(r-G) where the sum is over G (reciprocal lattice vectors)?
  34. B

    Using Poincare Bendixson's Theorem to prove a periodic Orbit

    Homework Statement The System is x˙ = 2x -y - x(x^2+y^2) y˙ = 5x - 2y(x^2+y^2) Using a trapping region to show there is a periodic orbit Homework Equations Use Poincare Bendixson's TheroemThe Attempt at a Solution I tried constructing 2 Lyapunov type functions to show that DV/dt>0 and...
  35. Y

    Periodic Motion and Simple Harmonic Motion Terminology Question

    In lecture, we are beginning to learn about waves and periodic motion under simple harmonic motion. We were given the equations: x=Acosθ and θ=ωt+\phi -- Substituting, we get x=Acos(ωt+\phi). This is simple enough; however what is Phi? All I was told is that "phi is a constant that allows us...
  36. O

    Periodic Solution to FIrst Order ODE Proof

    Homework Statement Consider the differential equation x' = f(t,x) where f(t,x) is continuously differentiable in t and x. Suppose that f(t+T,x) = f(t,x) for all t Suppose there are constants p, q such that f(t,p) > 0, f(t,q) < 0 for all t. Prove that there is a periodic solution...
  37. J

    Power contained in a periodic signal (complex exponentials)

    Compute the power contained in the periodic signal x(t) = 10.0[cos(160.7πt)]^4 The problem I have is I end up with a constant value for ak for all values of k -I start by using inverse Euler formula -Do the appropriate integration -Then consider k for odd and even values My working is...
  38. P

    Cam Lift as a Periodic Forcing Function

    Homework Statement Background: Given a cam and follower system in the valvetrain of an internal combustion engine and a table of values relating follower lift with respect to angular displacement, I would like to model the input delivered to the valvetrain by the cam lobe as a periodic forcing...
  39. M

    Criteria of periodic boundary condition

    We used to apply periodic boundary condition to simulate an infinite system. What will happen if the interactions between atoms do not drop to zero even when they are infinitely far away? Is the periodic boundary still valid? How can I prove the periodic boundary condition is valid or not? thanks.
  40. Fernando Revilla

    MHB F continuous and {f(x)} = f({x}) implies f(x) or f(x)-x periodic

    I quote an unsolved problem from another forum posted on January 8th, 2013.
  41. A

    Solving SE Numerically for Periodic Potential

    Okay so I am solving the SE numerically for different potentials. Amongst those I am trying to find the low energy wave functions for a periodic potential of the form: V=V0cos(x) Now recall that for a numerical solution, at least the type I am doing, you somehow have to assume that the wave...
  42. K

    Periodic force applied to pendulum-like motion

    When a force is applied to a pendulum, the pendulum sways back and forth until it eventually stops. In this problem however, a force is applied at uneven time intervals while the pendulum is still in motion. The force is always applied in the same direction. A data set is given containing...
  43. J

    Converting periodic function from radians to time?

    Homework Statement Hey guys. So I have this homework exercise where I have to convert the following periodic function in radians into a periodic function in time. f(θ) = (80/∏2) θ, -∏/2 ≤ θ ≤ ∏/2 (80/∏) - (80/∏2) θ, ∏/2 ≤ θ ≤ 3∏/2 Homework Equations θ = ω0 t ω0 = 2∏/T...
  44. S

    Convolution of periodic signals

    Homework Statement Consider an LTI system with impulse response h(t) = (0.5sin(2t)/(t) Find system output y(t) if x(t) = cos(t) + sin(3t) Homework Equations y(t) = x(t)*h(t) The Attempt at a Solution I am only familiar with doing much simpler convolutions using graphical...
  45. P

    Is cosx+cos(sqrt(2)x) periodic?

    Homework Statement Is the function cosx + cos(sqrt(2)x) is periodic? Homework Equations cos(x)=cos(x+2pi) The Attempt at a Solution For the above function to be periodic: cosx + cos(sqrt(2)x) = cos(x+T) + cos(sqrt(2)(x + T)) Does that imply that 2pi = T AND 2pi = sqrt(2)T, ergo...
  46. E

    Sequences of periodic functions converging to their average value

    Homework Statement Let f be a 2π-periodic function (can be any periodic really, not only 2π), and let g be a smooth function. Then lim_{n\rightarrow∞}\int^{B}_{A} f(nx)g(x) converges to \frac{1}{2π}\int^{2π}_{0}f(x) The Attempt at a Solution So far, I've come up with somewhat of...
  47. D

    MHB Continuous periodic piecewise differentiable

    Suppose that $f(\theta)$ is a continuous periodic piecewise differentiable function. Prove that $f(\theta) = f(0) + \int_0^{\theta}g(t)dt$ for a piecewise continuous $g$. I just need a nudge in the right direction here.
  48. S

    Can I define frequency for an non periodic signal?

    Do non periodic signals have frequency? Because my pretty general rule f = 1/T says that they have zero frequency. But suppose i analyze a voice signal. We generally associate a term frequency with them. If you ever had used audacity you might have noticed that the graph is quite...
  49. M

    Atomic weight and noble gases in Mendelev's periodic table

    Why did Mendelev order the elements according to their atomic masses rather than their atomic number? Why did Mendelev not include noble gases in his periodic table?
  50. E

    How i can plot anti periodic sine wave in matlab ?

    i don't know how i can use MATLAB to plot anti periodic fun .. the origin site give this code for triangular fun: fs = 10000; t = -1:1/fs:1; x1 = tripuls(t,20e-3); plot(t,x1), xlabel('Time (sec)');ylabel('Amplitude'); title('Triangular Aperiodic Pulse') but when i use this for sine...
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