Hydrogen atom - radial wave function normalization

R(r)=Nr^l e^(-Zr/na) ∑_(j=0)^(n-l-1)▒〖b_j r_j 〗 Finding the normalization constant: Rodriguez formula for associated Laguerre formula is: (e^x x^(-k))/n! d^n/(dx^n ) (〖e 〗^(-x) x^(n+k) )=(e^x x^(-k-n))/n! x^n d^n/(dx^n ) (〖e 〗^(-x) x^(n+k) ) R(r)=∫_0^∞▒(Nr^l e^(-Zr/na) (...

Finding exoplanet mass & distance from radial velocity data

Observations TABLE 1: 51 Pegasi Radial Velocity Data Day v (m/s) Day v (m/s) Day v (m/s) Day v (m/s) 0.6 -20.2 4.7 -27.5 7.8 -31.7 10.7 56.9 0.7 -8.1 4.8 -22.7 8.6 -44.1 10.8 51 0.8 5.6 5.6 45.3 8.7 -37.1 11.7 -2.5 1.6 56.4 5.7 47.6 8.8 -35.3 11.8 -4.6 1.7 66.8 5.8 56.2 9.6 25.1 12.6 -38.5 ...

Commutation Relations of the Angular Momentum Operators

Consider a particle described by the Cartesian coordinates (x,y,z) = X and their conjugate momenta (px, py, pz) = p. The classical definition of the orbital angular momentum of such a particle about the origin is L = X x p. Let us assume that the operators (Lx, Ly, Lz) = L which represent the com...

Size Matters: Introduction to Nanoscience and Nanotechnology

Question: Calculate the proportion of atoms on the surface atomic layer of Ag spheres with the diameters below given that the thickness of the surface atomic shell is 0.289nm, stating any assumptions made. a) 1 micro meter b) 10 nm c) 5 nm

The Concept of Nearest Neighbours

I'm having trouble understanding the concept of "nearest neighbours" and "next nearest neighbours." I understand that the number of nearest neighbours is the number of atoms per unit cell, but that's all I know (and I'm not sure why). I'd like someone to show me how to calculate the number of n...

X-Ray diffraction and lattice constant

a) Consider a crystal structure like that of NaCl, but unlike NaCl in this crystal all atoms are of the same type. Assume that x-rays of = 1[nm] are incident at =30° to the surface of the crystal. What is the lattice constant (distance between neighboring atoms) of the cubic crystal? b)...

Tunneling

A Hydrogen atom and a Helium atom each with 4 eV of KE approach a thin barrier 6 MeV high which has the greater probability of tunneling through the barrier? Explain.

Linear Momentum and Collisions

A neon atom (m = 20 u) makes a perfectly elastic collision with another atom. After the impact, the neon atom travels away at a 54.4° angle from its original direction and the unknown atom travels away at a 50.0° angle. What is the mass of the unknown atom?

Matter Wave Question

When the spectrum of once-ionized helium, He+, was first observed, it was interpreted as a newly discovered part of the hydrogen spectrum. The following two questions illustrate this confusion: (a) Show that alternate lines in the Balmer series of He+ - that is, those lines given by the Rydberg form...