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Chapter 8: Problem 43

Describe how the Bohr model of the hydrogen atom appears to violate the Heisenberg uncertainty principle.

Short Answer

Expert verified
The Bohr model appears to violate the Heisenberg uncertainty principle as it posits that an electron moves in definite orbits around the nucleus (implying a certain position and momentum), while the Heisenberg principle states that the position and momentum of a particle cannot be simultaneously determined.

Step by step solution

01

Understand the Bohr Model

In the Bohr model of the atom, electrons move in defined concentric orbits around the nucleus. The position and momentum of an electron can be calculated at any given point if the electron is observed to be in one of these orbits.
02

Understand the Heisenberg Uncertainty Principle

The Heisenberg Uncertainty Principle, a fundamental concept in quantum mechanics, states that we cannot precisely measure both the position and momentum of a subatomic particle, like an electron, at the same time. The act of measuring one quantity makes the other more uncertain.
03

Identify the Violation

In step 1, the Bohr model implies that the position and momentum of an electron can both be known simultaneously since it is in a definite orbit. This directly contradicts the Heisenberg uncertainty principle described in step 2, which asserts we cannot know both quantities at the same time. Therefore, it appears as if the Bohr model is violating the Heisenberg uncertainty principle.

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Most popular questions from this chapter

Based on the relationship between electron configurations and the periodic table, give the number of (a) outer-shell electrons in an atom of \(\mathrm{Sb} ;\) (b) electrons in the fourth principal electronic shell of \(\mathrm{Pt} ;\) (c) elements whose atoms have six outer-shell electrons; (d) unpaired electrons in an atom of Te; (e) transition elements in the sixth period.

What type of orbital (i.e., \(3 s, 4 p, \ldots)\) is designated by these quantum numbers? (a) \(n=5, \ell=1, m_{\ell}=0\) (b) \(n=4, \ell=2, m_{\ell}=-2\) (c) \(n=2, \ell=0, m_{\ell}=0\)

Radio signals from Voyager 1 in the 1970 s were broadcast at a frequency of 8.4 GHz. On Earth, this radiation was received by an antenna able to detect signals as weak as \(4 \times 10^{-21} \mathrm{W}\). How many photons per second does this detection limit represent?

Although Einstein made some early contributions to quantum theory, he was never able to accept the Heisenberg uncertainty principle. He stated, "God does not play dice with the Universe." What do you suppose Einstein meant by this remark? In reply to Einstein's remark, Niels Bohr is supposed to have said, "Albert, stop telling God what to do." What do you suppose Bohr meant by this remark?

Briefly describe each of the following ideas or phenomena: (a) atomic (line) spectrum; (b) photoelectric effect; (c) matter wave; (d) Heisenberg uncertainty principle; (e) electron spin; (f) Pauli exclusion principle; (g) Hund's rule; (h) orbital diagram; (i) electron charge density; (j) radial electron density.
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