How do you convert quantum numbers; such as n=3, L=2, m=+1, s=-1/2
Convert them to what?
http://en.wikipedia.org/wiki/Principal_quantum_number
To convert quantum numbers, you need to understand their meanings and equations. Let's break down each quantum number and see how they can be converted.
1. Principal Quantum Number (n):
The principal quantum number represents the energy level or shell of an electron in an atom. It can take any positive integer value (1, 2, 3, and so on). In your example, n = 3, which means the electron is in the third energy level.
2. Azimuthal Quantum Number (L):
The azimuthal quantum number determines the shape of the electron's orbital within a given energy level. It can take integer values ranging from 0 to (n-1). The corresponding orbital shape can be determined using the following convention:
L = 0 corresponds to an s orbital (sphere-shaped)
L = 1 corresponds to a p orbital (dumbbell-shaped)
L = 2 corresponds to a d orbital (clover-shaped)
L = 3 corresponds to an f orbital (complex shape)
In your example, L = 2, so the electron is in a d orbital.
3. Magnetic Quantum Number (m):
The magnetic quantum number specifies the orientation of an orbital within a subshell. It can take integer values ranging from -L to +L. For example:
m = -L corresponds to the orbital being oriented along the x-axis
m = 0 corresponds to the orbital being oriented along the z-axis
m = +L corresponds to the orbital being oriented along the y-axis
In your example, m = +1, so the d orbital is oriented along the y-axis.
4. Spin Quantum Number (s):
The spin quantum number describes the intrinsic spin of the electron. It can have two possible values: +1/2 (spin-up) or -1/2 (spin-down). In your example, s = -1/2, so the electron has a spin-down configuration.
Overall, your quantum numbers indicate that the electron is in the 3rd energy level (n = 3), in a d orbital (L = 2), with an orientation along the y-axis (m = +1), and a spin-down configuration (s = -1/2).