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 = h2/8ml2 = (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...
According to the Quantum Theory model of an atom, we can’t point out where an electron is. Moreover, we can’t determine the electron’s velocity and its position with the same degree of accuracy. True or False
2. In classical mechanics, we learned that particles undergoing some sort of orbital or circular motion have angular momentum. For ordinary momemtum, we learned that the conservation of momentum occurs because a system is translation invariant. It is possible to show (we won't do it here in complete generality) that a classical mechanics system has conserved angular momentum if it is rotation invariant. In classical mechanics angular momentum L is given by In this problem we're going to work out...
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...
QM 30 Relating classical and quantum mechanics IV. Supplement: Highly-excited energy eigenstates A particle is in the potential well shown at right A. First, treat this problem from a purely elassical standpoint (assume the particle has enough energy to reach both regions) Give an example of a real physical situation that corresponds to this potential well. 1. region I | region II 2. In which region of the well would the particle have greater kinetic energy? Explain. 3. In which...
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...