Compare the calculated zero-point energies according to Quantum Mechanics and Classical Mechanics for a xenon atom confined to a 10 nm line.
according to Quantum Mechanics
ZPE = h^{2}/8ml^{2} = (6.626 x 10^{-34})^{2} /{8 x 9.1 x 10^{-31} x (10 x 10^{-9})^{2}} = 6.0308 x 10^{-22} J
According to according to Quantum Mechanics ZPE = 0 (energy at 0 K is ZPE)
Compare the calculated zero-point energies according to Quantum Mechanics and Classical Mechanics for a xenon atom...
A hydrogen atom is in the n = 6 state. Determine, according to quantum mechanics, (a) the total energy (in eV) of the atom, (b) the magnitude of the maximum angular momentum the electron can have in this state, and (c) the maximum value that the z component Lz of the angular momentum can have.
What is the zero point energy? How does this differ from classical mechanics? Give examples where the zero point energy can be found.
-36 Imagine an alternate universe where the value of the Planck constant is 6.62607x 10J- In that universe, which of the following objects would require quantum mechanics to describe, that is, would show both particle and wave properties? Which objects would act like everyday objects, and be adequately described by classical mechanics? object quantum or classical? classical A human with a mass of 70. kg, 2.4 m high, moving at 4.5 m/s. quantum classical A ball with a mass of...
9. According to quantum mechanics, we must describe the position of electron in the hydrogen atom in terms of probabilities. (a) What is the difference between the probability density as a function of r and the radial probability function as a function of r?(2 pts) (b) What is the significance of the term 4nr2 in the radial probability functions for the s orbitals?(2 pts) (c) Make sketches of what you think the probability density as a function of r and...
3. Correspondince between classical and quantum mechanics (a) Assuming the Hamilton operator HV(c) show that This problem can be solved very similarly to what we had done in class for 2). Note that for this you may want to expand the potential energy operator V() in terms of the position operator x as V( a1+ After having dealt with the first few terms of the expansion, you probably will realize that it may be useful to find a general expression...
Zeolites are crystalline structures of aluminum, silicon and oxygen with pores that can act as cages or channels for molecules. They are often used for separating molecules by their size. Answer the next four questions to determine if classical mechanics are sufficient to model a helium atom traveling through a zeolite. What is the de Broglie wavelength for a helium atom (m = 6.6 x 10-27 kg) traveling at v = 1000 m/s (typical speed for an He atom at...
The energy E of the electron in a hydrogen atom can be calculated from the Bohr formula: E=- In this equation R, stands for the Rydberg energy, and n stands for the principal quantum number of the orbital that holds the electron. (You can find the value of the Rydberg energy using the Data button on the ALEKS toolbar.) Calculate the wavelength of the line in the absorption line spectrum of hydrogen caused by the transition of the electron from...
Questions Energy levels in the Bohr Hydrogen Atom In this section we will calculate energies for orbits (energy levels) of the Bohr hydrogen atom using the following relationship: - -2.178 x 10- 26) where is the energy (in joules) and is the electron energy level. Allowable values for nare are non-zero, positive integers (1, 2, 3......0). 1) For each value of 2, calculate the energy of the orbit in joules. Please show your work for the calculations for 1 =...
- Explain the trends in the magnitude of your errors for (a) the H atom and (b) the He^+ ion. It is presented without derivation in Equntion 3.3 (3.3) ( )--(2. 178 x10-i, J)를 where n identifies the orbit whose energy is belng caleulated; 2 is the atonie number of the atom or on eketron ion: m, is the mi of the electron; ro is the vacuum permittivity: e is the charge on the electron; and h is Planck's constant....
In this optional assignment you will find the eigenfunctions and eigenenergies of the hydrogen atom using an operator method which involves using Supersymmetric Quantum Mechanics (SUSY QM). In the SUSY QM formalism, any smooth potential Vx) (or equivalently Vr)) can be rewritten in terms of a superpotential Wix)l (Based upon lecture notes for 8.05 Quantum Krishna Rajagopal at MIT Physics II as taught by Prof Recall that the Schroedinger radial equation for the radial wavefunction u(r)-r Rfr) can be rewritten...