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Purdue university in its article on Bohr's Model explains:

At first glance, the Bohr model looks like a two-dimensional model of the atom because it restricts the motion of the electron to a circular orbit in a two-dimensional plane. In reality the Bohr model is a one-dimensional model, because a circle can be defined by specifying only one dimension: its radius, $r$. As a result, only one coordinate (n) is needed to describe the orbits in the Bohr model.

Could someone please elaborate the point that how Bohr's Model is One-Dimensional?

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    $\begingroup$ The 100th birthday of the correct formulation of quantum mechanics (by Heisenberg and Schrödinger) will be next year. It is time to forget the Bohr model (R.I.P.). It is simply wrong... $\endgroup$
    – Hyperon
    Commented Feb 21 at 8:58
  • $\begingroup$ @Hyperon I guess that it's a good way to introduce quantum ideas at a first or second year QM course. $\endgroup$
    – Gabriel Ybarra Marcaida
    Commented Feb 21 at 10:02
  • $\begingroup$ remember rsquar=xsquare+ysquare+zsquare. 3-D $\endgroup$
    – SAKhan
    Commented Feb 21 at 13:25
  • $\begingroup$ @GabrielYbarraMarcaida No, it's simply a waste of time and causes a lot of confusion to follow the historic path. Simply tell people the truth and start with QM proper. In my own course on QM, I spend only the first five minutes on the prehistory of quantum theory. That's more than enough. We are not historians of science. $\endgroup$
    – Hyperon
    Commented Feb 21 at 15:20

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He simply means, as stated in the article, that you can completely specify the orbit with only one parameter (the radius $r$, or the quantum number $n$).

This doesn't that the system lives in one spacial dimension, which I fear was your confusion. It lives in three, as it is the real world!!!

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It is clearer to describe the Bohr model of the electron as having one degree of freedom, so as to avoid confusion between the number of spatial dimensions and the number of dimensions in the electron's phase space.

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This isn't a physics question but a math question,

What the article means to say is that a circle is a 1D entity because you only need one dimension to describe a circle, if we're talking about the area of a circle it's indeed 2D but if we're only talking about its curve it's a 1D entity.

The same way a sphere's also a 2D entity if you're talking about the curve (which is also referred to as surface area) but the volume is a 3D entity.

Now you may argue that we represent a circle by $(x-x_1)^2$ + $(y-y_1)^2$ = $a^2$ but please do remember that we define a line which was supposed to be a 1D entity with y = mx +c.

We define both 1D figures with 2 variables.

You can't define an entity's dimension on the basis of the number of dimensions it resides in. For example you can make a line exist in 3D as well.

enter image description here

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  • $\begingroup$ I got the point that path of electron is one-dimensional but considering elctron and nucleus a whole system (atom) is it 1-d or 2-d? $\endgroup$
    – Govind Prajapat
    Commented Feb 21 at 13:04
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    $\begingroup$ It is clear from context in the OP that "one-dimensional" refers not to the dimensionality of a circle but to the dimensionality of a moduli space of circles. $\endgroup$
    – WillO
    Commented Feb 21 at 14:48
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It would be better to call it a discrete model, or even zero-dimensional, since Bohr does not consider a continuous range of radii but only discrete levels. There are no superpositions of states "in between" the levels, the transit between states where they would occur was not described by Bohr.

Since the model was mainly behavioral, it is difficult to argue what exactly is the underlying reality, so questions like this have no decisive answer.

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