Quantum Mechanics and Electron Configuration in a Modified Universe

[name_ask17]

Homework Statement

In a universe different from ours, the laws of quantum mechanics are the same as ours with one small change. In this different universe the m ℓ quantum number obeys this rule.

mℓ = (-ℓ-1), (-ℓ),..,0,...(ℓ), (ℓ+1)

In this different universe, what is the maximum number of electrons required to fill the 2p orbitals?

Determine only the electrons in the indicated p orbitals not any in other orbitals

The Attempt at a Solution

How do I do this question? I though m ℓ didn't affect the number of electrons in the p orbitals, so i put that the answer for the maximum number of electrons in 2p orbital was 6, however that was wrong. So, how do I do this? How does the m ℓ affect the maximum number of electrons? Would the answer be 10, since m ℓ would be values of -2, -1, 0, 1, 2? This really makes no sense to me. Any help would be appreciated. Thanks in advance.

 

[Borek]

Would the answer be 10, since m ℓ would be values of -2, -1, 0, 1, 2?

That's the intended logic behind.

It makes exactly as much sense as three orbitals for three possible m_l values of -1, 0, 1 (at least as long as you don't know where the rule limiting possible values of m_l comes from).

 

[name_ask17]

But i don't understand. Does each m ℓ value correspond to 2 electrons? Like in a normal universe?

 

[Borek]

Yes.

 

[name_ask17]

I don't follow this logic. For example, if it was 3p insetead of 2p, m ℓ would be -2, -1, 0, 1, 2 in normal universe. This would mean the max is 10, which is not true. The max is still 6.

 

[Borek]

The way it works here is that we always have three p orbitals (regardless of n) - usually denoted p_x, p_y and p_z. But we can write them as p_-1, p₀ and p₁ as well. In the other universe there would be p_-2, p_-1, p₀, p₁ and p₂.

Perhaps you are confused by the fact that "orbital" can mean either 3p or 3p_x (or just p_x, without any more detailed specification).

 

[AGNuke]

What's the value of m for 3p. Its 1. So, the values of l are -1, 0 and +1.

You took it wrong. Think again!

 

[name_ask17]

ohh right. yes, i was thinking of it wrong. but if i have something like 2s. then l= 0, and ml is also 0, right? so there's only 1 possible ml value there, so according to the original question, in a regular universe the max electrons is 2, so in this alternate universe, it would also be 2?

 

[AGNuke]

Since it is not stated that each orbital can hold x electrons, so yes, its 2.