The postulates of the Bohr model of the hydrogen atom can be stated as follows:
I. The electron can exist only in discrete states each with a definite energy.
II. The electron can exist only in circular orbits.
III. The angular momentum of the electron is nh/2pi where n is any positive integer.
a. State whether each of these postulates is currently considered to be correct, according to the wave mechanical description of the hydrogen atom.
b.Give the wave mechanical description that has replaced one of the postulates now considered to be incorrect.
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I read (or at least tried to read) through the wave mechanical description in my textbook, but the only thing I got out of it is that II is correct. My hunch is that III is incorrect, but I don't know for sure. Help please?
Thank you!
I and III remain correct in quantum throey. Orbits are not circular, however. Electrons really do not follow orbits at all.
The orbits with the highest angular momenta are the least circle-like in their wave function symmetry. For a while, the Bohr model was modified to include elliptical orbits, but they are not realistic either.
According to the wave mechanical description of the hydrogen atom:
a. Postulate I is considered to be correct. The concept of discrete energy levels or states, known as quantum states or energy levels, still holds true in quantum mechanics. The electron in an atom can only exist in these specific energy states.
b. Postulate III is considered to be incorrect. The wave mechanical description of the hydrogen atom replaced the notion of the electron's angular momentum being quantized at nh/2π, as proposed by Bohr. In quantum mechanics, the angular momentum of an electron is quantized, but it is given by a slightly different formula: √(l(l+1))h/2π, where l is the orbital quantum number that can range from 0 to (n-1), where n is the principal quantum number.
I hope this clarifies your question. Let me know if you need further assistance!
Sure! Let's break down the postulates and see if they are considered correct according to the wave mechanical description of the hydrogen atom:
I. The electron can exist only in discrete states each with a definite energy.
- According to the wave mechanical description, this postulate is indeed considered correct. In the wave mechanical model, electron energy levels are quantized, meaning that electrons can only exist in specific energy levels or states. These energy states are determined by the solutions to the Schrödinger equation.
II. The electron can exist only in circular orbits.
- This postulate is considered incorrect in the wave mechanical description. In the Bohr model, it was assumed that the electron moved in well-defined circular orbits around the nucleus. However, in wave mechanics, electrons are described by wavefunctions, which represent the probability distribution of finding an electron in a particular region of space. The wavefunctions do not correspond to classical circular orbits but rather to cloud-like regions where the electron is likely to be found.
III. The angular momentum of the electron is nh/2pi where n is any positive integer.
- This postulate is also considered incorrect in the wave mechanical description. In the Bohr model, it was assumed that the angular momentum of the electron was quantized and could only take on specific values that were multiples of nh/2pi. However, in wave mechanics, the angular momentum of the electron is not restricted to these discrete values. The actual values of angular momentum are determined by the solutions to the Schrödinger equation and can be any real number.
In summary:
- Postulate I is correct in the wave mechanical description.
- Postulate II is incorrect in the wave mechanical description.
- Postulate III is also incorrect in the wave mechanical description.
I hope this helps clarify the differences between the Bohr model and the wave mechanical description of the hydrogen atom!