Bohr Model of Atom: Stability Condition Explained

In summary, Eisberg and Resnick explain that the condition for stability of an atom is represented by the equation k Ze2/r2=mv2/r. The Z represents the number of electrons and protons in the atom and is left open to accommodate different types of atoms. The given equation is actually the classical F = ma equation for circular orbits, while the stability condition is Bohr's condition: mvr = n\hbar.
  • #1
connor415
24
0
Eisberg and Resnick says that the condition for stability of the atom is:

k Ze2/r2=mv2/r

What I fail to understand is why the Z isn't square too. I mean surely you have Z electrons interacting with Z protons which which would surely give q1q2=(Ze)(-Ze)=-Z2e2?

What am I missing?
 
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  • #2
No. They are dealing with a one electron atom. You might say: then it's hydrogen, so why not put Z = 1? They leave Z open so the same treatment will do for, an He+ ion and so on.

Incidentally the equation you give isn't really the condition for stability. It is the classical F = ma equation for circular orbits. The stability condition is Bohr's condition: mvr = n[itex]\hbar[/itex].
 

1. What is the Bohr Model of Atom?

The Bohr Model of Atom is a simple model of the atom proposed by Danish physicist Niels Bohr in 1913. It describes the atom as a small, positively charged nucleus surrounded by orbiting electrons at specific energy levels.

2. How does the Bohr Model explain stability of an atom?

The Bohr Model explains that atoms are stable when electrons occupy specific energy levels or orbits around the nucleus. These energy levels are quantized, meaning they can only have certain values, and the electrons are restricted to these levels. This results in a balance of attractive and repulsive forces between the nucleus and electrons, leading to the stability of the atom.

3. What is the stability condition in the Bohr Model of Atom?

The stability condition in the Bohr Model states that an atom is stable when the angular momentum of an electron is an integer multiple of Planck's constant divided by 2π.

4. How does the Bohr Model explain the line spectra of atoms?

The Bohr Model explains the line spectra of atoms by proposing that electrons can only exist in specific energy levels, and when they transition from a higher energy level to a lower one, they emit a specific amount of energy in the form of light. This emitted light corresponds to a specific wavelength, resulting in the observed line spectra.

5. Is the Bohr Model still considered accurate in modern atomic theory?

No, the Bohr Model is considered an oversimplified model of the atom and has been replaced by more complex and accurate models, such as the quantum mechanical model. However, it still provides a foundational understanding of atomic structure and is often used to introduce the concept of atomic theory in introductory science courses.

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