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Chapter 4: Problem 123

What is wrong with Bohr's planetary model of atomic electrons according to modern quantum mechanical theory? (Hint: Use Heisenberg's uncertainty principle in your answer.)

Short Answer

Expert verified
The main flaw in Bohr's planetary model of atomic electrons is that it assumes the electrons have well-defined positions and momenta in fixed orbits, contradicting Heisenberg's uncertainty principle (\(\Delta x \cdot \Delta p \ge \dfrac{\hbar}{2}\)). Modern quantum mechanics, instead, uses the electron cloud model, which accounts for the uncertainty principle by describing the electron's position and momentum as probabilities rather than precisely defined values.

Step by step solution

01

Understand Bohr's Planetary Model

Bohr's planetary model suggested that electrons revolve around the nucleus in fixed, circular orbits. The electrons were assumed to have a known position and momentum at any given time, much like the planets revolving around the sun in our solar system.
02

Know Heisenberg's Uncertainty Principle

Heisenberg's uncertainty principle states that we cannot determine the exact values of a particle's position and momentum at the same time. This principle can be mathematically stated as: \(\Delta x \cdot \Delta p \ge \dfrac{\hbar}{2}\), where \(\Delta x\) represents the uncertainty in position, \(\Delta p\) represents the uncertainty in momentum, and \(\hbar = \dfrac{h}{2\pi}\) (Planck's constant divided by \(2\pi\)).
03

Apply the Uncertainty Principle to Bohr's Model

According to Bohr's model, electrons have well-defined positions and momenta as they revolve around the nucleus in fixed orbits. However, Heisenberg's uncertainty principle contradicts this, as it proves that it is impossible to know the precise position and momentum of the electrons simultaneously.
04

Explain the Modern Quantum Mechanics View

In modern quantum mechanics, the electron's position and momentum are no longer defined by fixed orbits. Instead, the electron's behavior is described by a probability cloud called an electron cloud or as a wave function. This model accounts for the uncertainty principle because electron's position and momentum are described as probabilities rather than precisely defined values.
05

Conclusion

The main flaw in Bohr's planetary model of atomic electrons according to modern quantum mechanics is that it assumes the electrons have well-defined positions and momenta, which contradicts Heisenberg's uncertainty principle. The modern view of atomic structure considers electrons as probability clouds, which better aligns with the uncertainty principle.

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