What is the Correct Formula for Calculating Angular Momentum in Bohr's Theory?

In summary, the conversation is discussing the concept of angular momentum for an electron in a 3d orbital in a hydrogen-like species. Answer 1 provides a formula for calculating angular momentum using the Bohr model, while Answer 2 suggests using the Schrödinger equation instead. The conversation also touches on the limitations of the Bohr model and the importance of using correct logic when answering questions. Ultimately, it is concluded that the Schrödinger equation should be used to calculate angular momentum for a 3d orbital in a hydrogen-like species.
  • #1
vkash
318
1
what is angular momentum of a electron in 3d orbital.
Answer 1: d=2 angular momentum = sqrt(2(2+1))* h/2*pie

If this answer is correct then it should correct for all the conditions.so see second answer.
Answer 2: what if i say that was excited hydrogen piece then it's angular momentum can also be written as 3*h/2*pie

Both the answer are not same what is wrong. How angular momentum of one electron has two values?
 
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  • #2
The Bohr model of the atom doesn't give the correct angular momentum.
 
  • #3
alxm said:
The Bohr model of the atom doesn't give the correct angular momentum.

I was expecting for such answer i have a reply for you that is in hydrogen like species energy of all the sub shells in a shell is equal so energy of 3d should equal to 3s then what will new angular momentum in 3s.
One more thing is always try to answer question with logic. without proper logic your answer is not useful.
One thing coming in my mind as it's solution is that, Is there any thing like d orbital for hydrogen like species.
 
  • #4
vkash said:
in hydrogen like species energy of all the sub shells in a shell is equal so energy of 3d should equal to 3s then what will new angular momentum in 3s.

I'm not sure what you're asking here. If you solve the Schödinger equation for the hydrogenic atom, the boundary conditions give you solutions for integer n = 1,2,3.. quantum numbers for the linear momentum, and l quantum numbers (such that 0 <= l <= n - 1) for the angular momentum, such that the states are 2l+1 degenerate. Those values of the linear momentum define a shell, those for angular momentum define a sub-shell. 3d is n=3, l=2 and 3s is n=3, l=0. If you're asking what n=3, l=1 is, then that's the 3p shell.
One more thing is always try to answer question with logic. without proper logic your answer is not useful. One thing coming in my mind as it's solution is that, Is there any thing like d orbital for hydrogen like species.
In the standard Bohr model, electronic states only have angular momentum, and incorrect values of it. It doesn't explain the degeneracy, or magnetic quantum number, or spin, or the fine and hyperfine interactions and many other things, it's also fundamentally at odds with real quantum mechanics; it's a semi-classical theory. The Bohr model is entirely incorrect in its physical description, it just happens to give the correct energy levels for the shells.

So where's the logic in comparing the results of theory known to be incorrect with the results derived from the theory that's known to be correct? The concept of 'orbitals' comes from the solutions to the Schrödinger equation for a hydrogenic atom, not the Bohr model.
 
  • #5
I want to say that if an electron is in 3d orbital in hydrogen like species then what is it's angular momentum? Which formula should i use Bohr's formula for schrodinger formula. A we know in hydrogen like species energy of 3s,3p,3d is equal so angular momentum should also equal.
From two replies it is coming as answer that Bohr's model is wrong for giving angular momentum and i should use this shrodinger formula (sqrt(l(l+1))* h/2*pie) to find angular momentum. (l is azimuthal quantum number.)
thanks for replying.
 

FAQ: What is the Correct Formula for Calculating Angular Momentum in Bohr's Theory?

What is Bohr's theory?

Bohr's theory, also known as the Bohr model, is a theory proposed by Niels Bohr in 1913 to explain the structure of an atom. It states that electrons orbit the nucleus in specific energy levels and can jump from one level to another by absorbing or emitting energy.

How is Bohr's theory different from other atomic models?

Bohr's theory differs from other atomic models, such as the Thomson and Rutherford models, in that it incorporates the concept of quantized energy levels for electrons rather than a continuous distribution of energy.

What is the main source of confusion with Bohr's theory?

The main source of confusion with Bohr's theory is the misconception that electrons orbit the nucleus in a circular motion, similar to planets around the sun. In reality, the electron's path is more accurately described as a wavelike motion within a specific energy level.

How does Bohr's theory explain the emission spectrum of atoms?

Bohr's theory explains the emission spectrum of atoms by stating that when an electron jumps from a higher energy level to a lower one, it emits a specific amount of energy in the form of a photon. The energy of the emitted photon corresponds to the difference in energy between the two levels, resulting in a unique spectral line for each element.

What are the limitations of Bohr's theory?

Bohr's theory has some limitations, including its inability to explain the behavior of atoms with more than one electron, such as helium. It also does not account for the wave-like nature of electrons, which is better explained by quantum mechanics. However, Bohr's theory was an important step in understanding the structure of atoms and laid the foundation for further developments in atomic theory.

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