Why is Bohr's model of an atom limited to explaining only the hydrogen spectrum?

[kay]

Why is Bohr's model of an atom not able to explain the spectrum of atoms other than hydrogen? Can you give an example? :what:

 

[mfb]

Is that homework?

Here is a hint: other atoms have more than one electron. Is this taken into account in the Bohr model?

 

[kay]

No, it isn't. While reading the chapter i encountered this line which says that Bohr's model can't explain the spectrum of atoms other than hydrogen.
But another doubt, can Bohr's model explain the spectrum of species isoelectronic to Hydrogen?

 

[mfb]

The Bohr model gives a reasonable approximation for light atoms (not molecules!) with just a single electron, yes.
It does not work well for heavy atoms due to relativistic effects and the size of their nuclei.

 

[kay]

Relativistic effects? :/

 

[jtbell]

Imagine a uranium nucleus with one electron, i.e. a U⁹¹⁺ ion. Calculate the orbital speed in the first Bohr orbit, assuming non-relativistic mechanics.

 

[kay]

I'm a student of 11th class. I have no idea. I don't even know orbitals had speed.
I don't know what is relativistic or anything. Sorry. I can't understand anything. :(

 

[jtbell]

Sorry, I thought you had at least seen a derivation of the Bohr orbit radii, which includes the orbital speed along the way. If you haven't, try the Wikipedia article on the Bohr model. It has enough information that you should be able to get the electron speed in orbit "n" with only a little bit of algebra.

The boundary between "non-relativistic" and "relativistic" is not sharp, but a common rule of thumb is that if a speed is greater than 0.1c, you really should be using relativistic equations.

 

[mfb]

I don't even know orbitals had speed.

They do not, but Bohr's orbits have a speed.

If that speed gets comparable to the speed of light ("c"), the formulas from classical mechanics (like kinetic energy = $\frac{1}{2}m v^2$) get imprecise to outright wrong and you have to consider special relativity.

 

[Phy_enthusiast]

You should first do study of different quantum numbers assigned to electrons in an atom,Bohrs theory was succesfu l in expaining hydrogen spectra at that time,but it was a rudimentary theory made out of Plancks law and observation of hydrogen spectra.