Quantum Mechanics Mcqs With Answers Pdf

[Tarja Rabito]

Almost all the threads (here and on Quora) state that the uncertainty principle prohibits the electron from entering the nucleus, for it would be required to travel with speeds greater than that of light, even though it has mass. However it is quite confusing, given that many support the probability of it being in the nucleus is not zero. Even if that is not true, wouldn't tunneling enable it to do it anyway?

I'd like to point out that this isn't a duplicate of Why don't electrons crash into the nuclei they "orbit"? as I am already aware of the quantum model, orbitals and principles like uncertainty and Pauli exclusion, and haven't been able to find a conclusive answer no matter where I've looked.

Its also different than What happens to Protons and Electrons when a Neutron star forms? although it's been a bit helpful (I think), but I am more interested in whether electrons and protons fuse into neutrons as soon as they get really close or there are more universal conditions than need to be satisfied before that happens (which obviously are in the specific case of neutron stars).

Edit: I wanted to get a bit more specific about the inconsistency I found. "In the quantum mechanical model of the electron, there is a finite probability of finding the electron within the nucleus. During the internal conversion process, the wavefunction of an inner shell electron (usually an s electron) is said to penetrate the volume of the atomic nucleus." Taken from the wikipedia page on internal conversion. Doesn't that come in conflict with the uncertainty principle based argument that the electron would have to travel faster than light?

Yet according to Why do electrons occupy the space around nuclei, and not collide with them? it does. I hope you can see how these two can confuse people. Thanks for anyone that answers it in advance.

As Feynman pointed out, the problem lies with the premises of the question which presupposes things like entering or leaving. These are notions common to a purely material atomic theory, where atoms enter a new configuration or leave one.

Whilst a neutron may decay into a proton and an electron, in no sense is a neutron ontologically speaking the same as a proton and an electron. The decay describes a process of ontological change. The neutron changes into a proton and an electron.

You might find it interesting that this one of the reasons that Aristotle dismissed the atomic theory, as he regarded such ontological changes as possible, and in fact neccessary, but the atomists merely saw change as a kind of permutation of matter; and this over two millenia ago!

All the references you refer to use a sort of semi-classical semi-quantum language, and you yourself admit you are confused about quantum mechanics. So it might be helpful to have a 'pure' quantum answer (although it might not directly address your question):

This sounds strange, since you can measure where the particle is (eg by constructing a box that tells you if there is a particle inside of it, then waiting until it beeps to signify the particle is in the box). Measurement is a complicated (and I think poorly understood?) process where an object so complicated that you need to resort to a classical system (the measuring device) interacts with a system you are trying to treat quantum mechanically. The result is tainted by the classical measurement device and you end up with classical notions like position in your output.

So the simple answer to the question is that no, an electron cannot be in the nucleus, because it cannot be anywhere. It does have a finite chance to be found in the nucleus if you were to measure it (again, imagine putting a box around the nucleus that tells you if there is an electron there, there is a finite chance it says yes). The fact that electron capture occurs means that the full quantum solution means there is a chance that the atom will later be found in a state which describes one less proton and electron and one more neutron. The semi-classical interpretation is that the electron spends a small fraction of its time in the nucleus (corresponding to whatever the probability of your magic measuring box saying it is there) and so there is a chance to "tunnel" in to the nucleus, fuse with an attractive proton and create a neutron. These semi-classical pictures can give accurate answers but they are not the full quantum picture.

Edit 1: Uncertainty PrincipleThe argument with the uncertainty principle is I believe being misapplied. Leaving aside any issues of interpretation, the uncertainty principle argument runs that if you locate the particle to be in the nucleus, then you must only know its momentum to some uncertainty:

Where $h$ is Planck's constant and $\Delta x$ is the uncertainty in our position measurement. If we are claiming to have measured the electron to be "in the nucleus" then we must have $\Delta x$ roughly the radius of the nucleus. (It's been pointed out in the comments that the notion of radius is not commensurate with positions not being quantum mechanical. That's okay, we're treating the nucleus classically here anyway.) This forces $\Delta p \sim \frach\Delta x$ and so the uncertainty in the particle's momentum becomes infinitely large as we try to confine the particle to a given location.

Then why, in hydrogen, does the electron not go closer to the nucleus than 1 angstrom? The reason is that in quantum mechanics the kinetic energy is proportional to the squared gradient of the orbital and increases faster than its potential energy decreases when it is shrunk.

The multiple-choice questions on the QMFPS were developed based on expert feedback about relevant topics, review of course materials and a subsequent test blueprint. The multiple-choice answers were developed based on research on student ideas about relevant quantum mechanics topics and the responses to a free-response version of the assessment that was given to students. The questions were tested with student interviews and revised. The QMFPS was then given to over 350 undergraduate and graduate students from 6 institutions, and appropriate statistical analysis of reliability, difficulty and discrimination were performed. Reasonable results were found. The results from the QMFPS have been published in one dissertation.

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Quantum mechanics (along with General Relativity) is one of the two foundational theories on which modern physics rests. PHYS2013 introduces the basic theoretical concepts and formalism, including the wave mechanics developed by Schroedinger and others and some aspects of the matrix formalism first developed by Heisenberg.

The course starts with an overview of the historical evidence that led to the development of a quantum theory of matter and light. This is followed by an introduction to the key elements of quantum mechanics, including the statistical interpretation of wave functions, the role of operators and their connection with observables, and uncertainty. These concepts are initially introduced and reinforced through relatively simple problems with analytic solutions, but computational solutions are also examined where appropriate.

PHYS2013 provides the foundations for further studies of, for example, atomic and nuclear spectroscopy, elementary particle physics and solid state physics as well as more advanced quantum mechanics. It is thus a core course in that it provides the background needed for several courses offered at third year. There is a small laboratory component (shared with PHYS2020).

This course is offered as an advanced option. The HPO/ASE for this course is a research assignment in the rapidly evolving area of non-Hermitian physics. You will be working on a familiar quantum system of a particle in an infinite square well but with gain or loss. In addition to analytical work, you will also learn a few numerical techniques in MATLAB to solve the problems. The HPO/ASE will count toward 25% of your mark, the rest of the assessment will be weighted at 75%.

The ANU uses Turnitin to enhance student citation and referencing techniques, and to assess assignment submissions as a component of the University's approach to managing Academic Integrity. While the use of Turnitin is not mandatory, the ANU highly recommends Turnitin is used by both teaching staff and students. For additional information regarding Turnitin please visit the ANU Online website.

For 1 hour each week I will meet with the class and discuss concepts in QM. Since this is the combination of a lecture and a tute, I call this a Lute. The main reason for this hour is for discussion of the assignment problems (hints not direct answers) as well as other similar problems.

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It is a PowerPoint presentation on numerical problems of Planck quantum theory topic. It includes 12 numerical problems with solved answers. Besides, this PowerPoint presentation has a mind map to remember all formulas of Planck quantum law.Read less

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