Separation Definition and 476 Threads

Homework Statement Want to separate two isotopes whose atomic masses differ by one neutron mass. We do this by filling a tube of height H with a gaseous mixture of the two isotopes Derive a formula of the enrichment factor [n1 (H)/ n2 (H)]/ [n1(0)/n2(0)] If the gas from the top of the...

Homework Statement if i have source separation between 2 light sources, d, and wavelength, λ, what is the highest order node and antinode? Homework Equations The Attempt at a Solution im not sure where to start for this question I am leaning towards division to cancel out the meters

Homework Statement use separation of variables to solve the differential equation x^2dy/dx=y-xy with the initial condition of y(-1)=-1 Homework Equations The Attempt at a Solution after i separated and integrated i got the answer y=e^(-1/x-lnx+c) the answer in the book is y=e^-(1+1/x)/x i...

\displaystyle\frac{dN}{dt} = rN\left(1-\frac{N}{K}\right)\displaystyle\int\frac{KdN}{N\left(K-N\right)} = \int rdt \displaystyle K\int\frac{dN}{N}-K\int\frac{dN}{K-N}=r\int dt Now, I obtain: K\ln\left(\frac{N}{K-N}\right) = rt+c \left(\frac{N}{K-N}\right)^K=C_0r^{rt} The final solution is...

Hello, Just out of curiosity, where would following "seperation axiom" fit in? So far I'm only acquainted with the T1, T2, T3 and T4 axioms (and the notion of completely regular in relation to the Urysohn theorem).

Homework Statement The question goes something like this: What % of inter atomic separation is the root mean amplitude. The data given is: Inter atomic separation : 0.29nm , T =300k , D = 20 N/m , Aluminium atomic weight 27 g/mole. How do I proceed I have no idea on how to relate mean...

This semester while taking Linear Programming (Linear Optimization Models), we talked about using a linear program to separate two sets of points A and B. The general program is: Max d s.t. yA ≥ axA+b+d yB ≤ axB+b-d It can be expanded into finding a polynomial that passes between the...

Homework Statement I made this problem up as an example for a bigger problem I have to do. P = {(-2,4),(1,3)} and Q = {(-1,1),(0,0)}. I need to use linear programming to find the best line to go between them. Homework Equations Max d subject to: y_{i}≥ax_{i}+b+d (for all points above...

Homework Statement I am having trouble understanding the concept of induced charge separation. In my textbook, there is a diagram that demonstrates the procedure, but it gets confusing because the first image is normal, and then it gets inverted? I don't understand in the second set-up if it...

I was just wondering if there are any written documents which give the views of the United States founding fathers' views towards separation of church and state. The constitution reads, "Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof"...

Two frictionless pucks are placed on a level surface at an initial distance of 20.0 m. The mass of puck 1 is 0.80 kg and it has a charge of +3.0 X 10^-4 C., while puck 2 is 0.40 kg with a charge of +3.0 X 10^-4 C. the initial velocity of puck 1 is 12.0 m/s (E) and the initial velocity of puck 2...

Homework Statement What is the minimum angular separation an eye could resolve when viewing two stars, considering only diffraction effects? Homework Equations θ=(1.22*λ)/D The Attempt at a Solution I tried estimating with λ=550 nm and D=5.0 mm (pupil diameter) which appeared in...

For my research purpose, I made a wind tunnel which has 0.6m rectangular section [0.2X0.2sq. meter] and 1.4m long diffuser section having porous top [top wall angle is 20deg] as follows: Wind tunnel speed is 15m/s. Even using 20deg inclination of porous top wall, there is no flow...

Homework Statement What is the minimum angular separation an eye could resolve when viewing two stars, considering only diffraction effects? Homework Equations Rayleigh criterion: θ=(1.22*λ)/D The Attempt at a Solution This problem doesn't give very much to go on so I think...

Hi everyone! I'm looking to separate nickel from a meteorite sample and I have a pretty solid plan... however I'd like to know if there are any disadvantages of using the following methods: Quinoxoline Complexation with Spectrophotometric Determination (using pre-separation to remove...

Homework Statement Using the method of separation of variables, obtain a solution of the following PDE subject to the given conditions \frac{du}{dx}+y\frac{du}{dy}=(2x+y)u u(x,1)=5e^{x^{2}-x} Homework Equations The Attempt at a Solution See my attached working the...

This isn't a HW problem, it's more of a general question. I'm reading Griffith's Intro to QM 3rd Edition. On page 134 he uses separation of variables, of which I'm familiar (but by no means an expert). Could someone explain why the separation constant in equations 4.16 and 4.17 changes sign...

Let's say I build a parallel plate capacitor using two metal plates with perfectly smooth surfaces. They are separated by some small distance d, with only vacuum between them. I then apply some AC voltage across the plates. Is there some effect which causes loss in the capacitor (equivalent...

Homework Statement Taking the equation of motion for a rocket launched from rest in a gravitational field g, m\dot{v} = -\dot{m}v_{ex} - mg , and knowing that the rocket ejects mass (fuel) at a constant rate \dot{m} = -k (where k is a positive constant), so that m = m_{o} - kt . Solve...

Homework Statement This is from Calculus for the Practical Man, by J.E. Thompson, 1962 edition. "Two automobiles are moving along straight level roads which cross at an angle of 60 degrees, one approaching the crossing at 25 mph, and the other leaving at 30 mph on the same side. How fast...

Dear Everyone, I have a question about the separation of variables for non-central potentials (r, \theta, \phi). In spherical coordinates, such a potential V(r,\theta)=u(r)+f(\theta)/r^2 can be separated. Who knows it could also be separated in other coordinates? Many thanks.

The cause-effect relationship of timelike events is fairly self-evident. But I was wondering, do non-local effects of QM "synchronise" events that are separated along spacelike intervals? Could there be some kind of co-dependent arising, such that if event X happens in one region of the...

Hi Everyone, I am trying to solve the partial differential equation given below: \Delta^2\phi(x,y,z)=\frac{qf(x,y,z)}{\epsilon} where f(x,y,z)=1 at one point and zero elsewhere. This is the poisons equation for a point charge inside a conducting box. Can this be solved using the...

Homework Statement Solve the following separable equation \frac{dy}{dx} = \frac{y}{x(x-1)} Homework Equations \int\frac{1}{x}dx=ln(x) The Attempt at a Solution See attachment Im getting y=(\frac{x-1}{x})^{c} as my answer when in fact the answer the tutor gave is...

Homework Statement Light consisting of two nearly equal wavelengths L and L+dL, where dL << L, is incident on a diffraction grating. The slit separation of the grating is D. Show that the angular separation of these two wavelengths in the m'th order is dTheta = dL / ((D/m)2+L2)0.5...

So I'm having trouble understanding how these two are related, i.e., how one proves the other. I understand the ideas behind both of them: For J-B, you're basically taking R^n and throwing in a sphere, so the inside of the sphere is bounded and everything outside the sphere is unbounded. For...

Dear all, Take my best wishes. I am facing a problem designing my experimental setup for my research. I want to produce flow separation over a flat plate. Here is my experimental setup: Diffuser angle is 16deg. I need some documentation/text book regarding the effect of suction flow rate...

Homework Statement The equilibrium separation of the atoms in H35CI equals 1.27 x 10-10m. Calculate the energy separation between adjacent lines in the rotational-vibrational spectrum Homework Equations E = (n + 1/2)h\omega + h2/ 2I * l(l+1) I = \mur02 \mu = m1m2/ m1 + m2 The...

Problem: The adjacent lines in the pure rotational spectrum of 35CI19F are separated by a frequency of 1.12 x 1010 Hz. What is the equilibrium separation of the atoms in this molecule? The attempt at a solution So, the equation I think I need to use to find the equilibrium separation...

The other day I found an article which proved the Jordan Curve Theorem using the van Kampen Theorem for the fundamental groupoid of a space. I was wondering if this technique could be extended to prove the more general Jordan-Brouwer Separation Theorem, using higher homotopy groupoids, the "van...

two frictionless pucks are placed on a level surface, as shown, at an initial distance of 20.0 m. the mass of puck 1 is 0.80 kg and it has a charge of +3.0 X 10^-4 C., while puck 2 is 0.40 kg with a charge of +3.0 X 10^-4 C. the initial velocity of puck 1 is 12.0 m/s (E) and the initial velocity...

Homework Statement Sorry don't know how to use the partial symbol, bear with me partial u wrt t=2*(2nd partial u wrt x) Boundary conditions: partial u wrt x (0,t)=partial u wrt x (1,t)=0 Initial conditions u(x,0)=x(1-x) Homework Equations I get an answer that is different...

For water separation purposes, what's the difference between steam and fully saturated air? I was looking at a certain product: http://www.nciweb.net/combinat.htm And I'm not sure if such a thing would be suitable for separating the water from a fully saturated air stream at about 60degC...

How might one try to separate water from air at high temperature (say, 75degC) - if the gas if fully saturated? I understand that you should try to cool it down first to do so, but other than putting it though a heat exchanger is there any other approach you can take? Thanks

One particle has a mass of 3.00 10-3 kg and a charge of +7.50 µC. A second particle has a mass of 6.00 10-3 kg and the same charge. The two particles are initially held in place and then released. The particles fly apart, and when the separation between them is 0.100 m, the speed of the 3.00...

\frac{\partial z}{\partial t}=\frac{\partial z}{\partial x}+\frac{\partial z}{\partial y} \mbox{Let }z=T(t)X(x)Y(y) T'(t)X(x)Y(y)=T(t)X'(x)Y(y)+T(t)X(x)Y'(y) \Rightarrow \frac{T'(t)}{T(t)}=\frac{X'(x)}{X(x)}+\frac{Y'(y)}{Y(y)} \Rightarrow \frac{T'(t)}{T(t)}=A \wedge...

Homework Statement http://i.imgur.com/mgIkS.png Two long parallel wires carry currents of 2.03 A and 8.83 A. The magnitude of the force per unit length acting on each wire is 4.49*10^5 N/m. Find the separation distance of the wires expressed in millimeters. Homework Equations I'm not...

Im doing separation of variables now and I am stuck...ive come up to this stage -5 ln 2-3i = t^2/2 + C my problem is do i need to divide the C and t^2/2 by -5? or don't divide the C? please help me.. thnks

Can anyone help me solve this ODE: ..in other words, find a general solution? dy/dx = e^(x+y) I use a separation method, but i can't take the natural log of -e^(-y). So, help?

Supposed you want to send an electron to a double slit. What must be the separation of the slits if they are say 1 meter away? What is the size of the initial electron field? When it travels to the slits, does the electron field expand in size? Why? I'm asking this because I'd like to know...

a) Derive a formula for solutions of the ode equation b) If (t0, x0) lies in the subset of the (t,x)-plane given by x>1 write down a formula for the unique solution of the equation below through this point. c)Give a formula for two solutions to equation below through the point (0,1) in the...

Homework Statement A scientist decides to do the double-slit experiment in a ver- tical tube, with the slits at the top and a viewing screen at the bottom as shown. With red light from a HeNe laser (632 nm) a nice pattern forms on the viewing screen, with the bright spots 1.50 cm apart...

See attached image for the question and my working. Hopefully you can read it OK, I had to resize it to fit to the allowed dimensions. I'm unsure how to proceed or if I have done something wrong previously - the initial and boundary conditions are tripping me up. The boundary conditions in red...

I've taken a first semester course on PDEs. Basically all we learned was separation of variables and method of characteristics. I understand that there are transforms out there, such as laplace and fourier. However, it looks like there aren't many analytical ways of solving PDEs. Mind you, I'm...

Just quick question about sep of variables.. say have function U(x,y)=X(x)Y(y) when do separation of variables end up with some generic case that looks like: X''/X=Y'/Y=lamda my question is (and I think I know now the answer but would like confirmation), is what sign should the lamda...

http://img835.imageshack.us/i/anmol.png/ the graph is as per the link but my question is that at a particular point the potential energy becomes zero...is thre any significance for it?

Homework Statement Use separation of variables to find a general series solution of u_t + 4tu = u_{xx} for 0 < x < 1, t> 0 and u(0,t) = u(1,t)=0. Homework Equations The Attempt at a Solution Looking for a solution of the form u(x,t) = X(x)T(t) implies that \frac{T'}{kt} - \frac{X''}{X} = 0...

Homework Statement Help solving this separation of variables. M(dv/dt) = [k*(v^2)] - Mg Homework Equations As above The Attempt at a Solution dv/(kv^2-Mg)= dt/M Intregrate both sides; (1/2kv) ln |kv^2-Mg|= t/m + c? Then what to do..? Something to do with with Ae^(-kt/M)..?

Homework Statement A free-falling sky-diver of mass M jumps from an aeroplane and beforen he opens his parachute experiences air resistance which is proportional to the square of the magnitude of his velocity. a) Show that the equation of motion for the sky-diver can be written as dv/dt = -g...

Homework Statement As part of the solution to a HW problem of mine, I have to solve the PDE p_t = -vk^2 p - k \delta p_k, where p = p(k,t) and v,\delta are known constants. Homework Equations I tried to look for a solution of the form p(k,t) = K(k)T(t) and found one, but I'm not sure if I...