Suppose you live in a different universe where different amount of quantum numbers is required to describe the atomic orbitals. These quantum numbers have the following rules:
N principal 1,2,3,….
L orbital =N
M magnetic -1. 0. +1
How many orbitals are there all together in the first electron shell?
I know that the number of orbitals in a subshell is 2L + 1, but, Im stuck after that.
Is a subshell the same as the orbitals in the first electron shell? Please explain if possible!
Thanks!
There is nothing in the problem that says the number of orbitals is 2L+1 is there? And since this is in another world I don't know that we can assume that is the number of orbitals. The way I see it is if L = N, then we have L=1 with subshells of -1, 0, and +1 which makes three orbitals, which, by the way, does agree with the 2L+1 idea.
In the provided universe, the rules for quantum numbers are given as follows:
- The principal quantum number (N) can take on values of 1, 2, 3, and so on.
- The orbital quantum number (L) is equal to the principal quantum number (N).
- The magnetic quantum number (M) can be -1, 0, or +1.
To determine the number of orbitals in the first electron shell, we need to consider the possible values for N and L. In this universe, N represents the principal quantum number and L represents the orbital quantum number.
In the first electron shell, the only allowed value for N is 1. According to the given rules, L will also be equal to 1 for the first electron shell.
Now we can calculate the number of orbitals in the first electron shell using the formula 2L + 1:
Number of orbitals = 2L + 1
= 2(1) + 1
= 2 + 1
= 3
Therefore, in this universe, the first electron shell would have 3 orbitals in total.
To address your question about subshells and orbitals: In the usual quantum mechanical description of atomic orbitals, subshells are subsets of orbitals within a given energy level (shell) that have the same value of L. However, in the provided universe, the concept of subshells is not mentioned. Therefore, we can assume that in this universe, subshells and orbitals are equivalent terms. In other words, the number of orbitals in a subshell is the same as the number of orbitals in an electron shell.
In this hypothetical universe, the rules for the quantum numbers are as follows:
- N (principal quantum number) can take values 1, 2, 3, and so on.
- L (orbital quantum number) is always equal to N.
- M (magnetic quantum number) can take values -1, 0, and +1.
To determine the number of orbitals in the first electron shell, we need to find the values of N and L for that shell.
In this universe, the first electron shell corresponds to N = 1. Therefore, L = 1 as well.
The formula for calculating the number of orbitals in a subshell is 2L + 1. In this case, since we have L = 1, we can substitute it into the formula:
Number of orbitals = 2(1) + 1
= 2 + 1
= 3
So, in the first electron shell in this universe, there are a total of 3 orbitals.
To clarify the terminology, a subshell refers to a specific orbital within a shell. For instance, in the first electron shell, there is only one subshell, which corresponds to the orbital with L = 1.
I hope this explanation helps you understand the concept of orbitals in this hypothetical universe. Let me know if you have any further questions!