The uncertainty principle and the hydrogen atom: Starting with
identify
from the uncertainty principle. Determine the minimum energy. How close is this to Bohr’s result?
The uncertainty principle and the hydrogen atom: Starting with identify from the uncertainty principle. Determine the...
(20 points) Treat the hydrogen atom as a one-dimensional problem, where the electron is confined to the diameter of the atom in the first excited state (n-2). a.) Use the uncertainty principle to estimate the minimum kinetic energy of an electron in this state, assuming that the uncertainty in position equal to it's diameter. (Note: Relativistic corrections are not necessary). b.) Assuming this excited electron only remains in this state for 0.1 ns, before emitting a photon and returning to...
Hydrogen atom. a. Given that the energy of the hydrogen atom depends only on the principle quantum number n, how many orbitals with a principle quantum number of n=4 are degenerate in energy? Use the quantum numbers associated with the solutions to the Schrödinger equation. (10 pts) b. List the quantum numbers of all orbitals that are degenerate in energy with the n=3, 1=2, m=-1 orbital. You may list in groups or a table to reduce the amount of repetitive...
If an electron's position is known with small uncertainty, then the Heisenberg Uncertainty Principle predicts that .. O its momentum can be known with a small uncertainty the uncertainty in its position divided by the uncertainty in its momentum is larger than a fixed value its momentum can only be known with a large uncertainty -/1 points Which is correct? O most of an atom's mass and volume are in the nucleus which has a positive charge most of an...
Exercise 7: Variational principle and hydrogen atom a) Variational method: show that EOT OTHOT)orloT) yields an upper bound to the exact ground state energy Eo for any trial wave function r. b) Apply the variational method to the ground state of the hydrogen atom (without rel- ativistic corrections), using as trial function r Ce"ar and compare it to the result of problem 7.13 of the book. c) The variational method can also be applied to excited states, by taking care...
In lab we studied the Bohr model of the hydrogen atom which is verified exactly with quantum mechanical calculations. From quantum mechanics we also find that Bohr’s equation can be used for any one-electron cation like He+, Li2+, Be3+ etc, by including the atomic number, Z, of the cation in the equation with Bohr’s constant (): En= -Z2n2(Accurate for any one-electron cation with atomic number Z) Use this equation to calculate the energy (J) of the first and second energy...
Does Bohr's theory of the hydrogen atom predict that it is possible for the electron in a hydrogen atom to orbit the nucleus with any possible radius? Yes, there are an infinite number of possible orbits, so that every radius is possible. O No, while there are an infinite number of possible orbits of different radii, the radii have only distinct values, not continuous values. O No, there are only a finite number of possible orbits of different radii. +-/1...
Use the Heisenberg uncertainty principle to calculate Ax for an electron with Av = 0.515 m/s. 5.89*10^(-5)m Ap = mav me = 9.10939x10-31 kg h = 6.62608x10-34 Js n = 3.14159265359... is. Tries 5/30 D uis žavit By what factor is the uncertainty of the (above) electron's position larger than the diameter of the hydrogen atom? (Assume the diameter of the hydrogen atom is 1.00x10-8 cm.) Tries 0/30 Use the Heisenberg uncertainty principle to calculate Ax for a ball (mass...
h where ħ=__=1.054 x 10-34 Js 27 Uncertainty principle Question) Uncertainty in position of an electron is 1 nm. Estimate the minimum uncertainty in momentum and the corresponding kinetic energy.
An excited hydrogen atom could, in principle, have a radius of 2.50 mm . Part A: What would be the value of n for a Bohr orbit of this size? Part B: What would its energy be?
An excited hydrogen atom could, in principle, have a radius of 2mm . Part A What would be the value of n for a Bohr orbit of this size? Part B What would its energy be? E= eV