Planck's Constant and the size of the atom

In summary, the uncertainty principle and the size of atoms would be affected if Planck's constant were smaller. The uncertainty principle would have decreased "uncertainness" and the size of atoms could be smaller than presumed due to decreased uncertainty in the position and velocity of electrons. However, the principle itself would remain unchanged.
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kirsten_2009
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2

Homework Statement


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If Planck’s constant were smaller than it is, how would the uncertainty principle be affected and how would the size of atoms be affected?

Homework Equations

The Attempt at a Solution



I know this question has been kind of asked before in this forum but an answer was never really concluded. Could you guys be so kind and let me know if my reasoning and answer are "correct"?

A:// Conceptually speaking; the uncertainty principle would be affected in that it’s “uncertainness” would be decreased because if the quanta of energy was smaller (since it was multiplied by a smaller number); it means that the space occupied by the field would be smaller and thus the position and/or velocity of an entity would be more accurately predicted since there is less space the species could actually be in.

With regards to the size of the atom; a smaller value for Planck’s constant would allow atoms to be smaller than presumed because the uncertainty of the electrons position (and velocity) would decrease and so the electron “cloud” could be narrowed down with increased accuracy and decreased error.
 
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What course are you doing and what handbook or notes is used?
 
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It's an introductory physics course focusing mainly on concepts (with some calculations of course). We are using Physics: Concepts and Connections by Art Hobson.
 
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The principle itself would not be affected I would think, but the product of the uncertainties in the values
- position, momentum, energy and time - would. Neither would the size of atoms, just the values would
be known with less uncertainty.
 
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This could potentially lead to the discovery of smaller subatomic particles within the atom or even a reevaluation of the current atomic model. However, it is important to note that the size of an atom is also influenced by other factors such as the number of protons and neutrons in the nucleus and the strength of the nuclear force. So while a smaller Planck's constant may have some impact on the size of the atom, it would not be the only determining factor.
 

What is Planck's Constant and how is it related to the size of an atom?

Planck's Constant, denoted as h, is a fundamental constant in quantum mechanics that relates the energy of a photon to its frequency. It is also used to calculate the energy levels of electrons in an atom. The size of an atom is determined by the average distance between the nucleus and the outermost electron, which is directly related to the energy levels of the electrons.

How was Planck's Constant first discovered and measured?

Planck's Constant was first discovered and measured by German physicist Max Planck in 1900. He was studying blackbody radiation, which is the electromagnetic radiation emitted by a heated object. Through his research, he found that the energy of a photon is directly proportional to its frequency and that the proportionality constant is Planck's Constant.

What is the value of Planck's Constant and how is it expressed?

The value of Planck's Constant is approximately 6.626 x 10^-34 joule seconds. It is expressed using the units of joule seconds (J·s) in the SI system of units. However, it can also be expressed in other units such as electron volts (eV) or erg seconds (erg·s).

How is Planck's Constant used to determine the size of an atom?

Planck's Constant is used in the calculation of the energy levels of electrons in an atom. The energy levels are determined by the distance between the nucleus and the electron, which is directly related to the frequency of the photon emitted or absorbed by the electron. By using the value of Planck's Constant, scientists can calculate the size of an atom.

Is Planck's Constant a universal constant?

Yes, Planck's Constant is considered a universal constant, meaning it has the same value throughout the universe. It is a fundamental constant in quantum mechanics and is used in many equations to describe the behavior of particles at the atomic and subatomic level.

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