Is this a possible quantum number:
3,2,2,-1/2
This is my thikning:
n=3
so therefore l = 0-2
so therefore ml could = 2
However, many of my classmates said it was impossible.
I agree with you. Have your classmates go through it like this.
n = 3
thus, l = 0, 1, or 2.
For l = 0, ml may be 0
For l = 1, ml may be -1, 0, or +1
For l = 2, ml can be -2, -1, 0. +1, or +2.
Then ms may be +/- 1/2
Thank you :)
To determine whether the given set of numbers is a possible quantum number, we need to follow the rules for assigning quantum numbers.
The quantum numbers in an atom describe the specific energy levels, orbital shapes, orientations, and spin of electrons. The four quantum numbers are:
1. Principal Quantum Number (n): It describes the energy level or shell in which the electron resides. It can have positive integer values (n = 1, 2, 3, ...).
2. Azimuthal Quantum Number (l): It denotes the subshell or orbital type within a given principal energy level. It can take the values from 0 to (n-1). The letters s, p, d, f correspond to l values of 0, 1, 2, and 3 respectively.
3. Magnetic Quantum Number (ml): It specifies the particular orbital within a subshell where an electron is most likely to be found. It can take values from -l to +l, including zero.
4. Spin Quantum Number (ms): It describes the spin direction of an electron, which can either be +1/2 (spin up) or -1/2 (spin down).
Now, let's analyze the given set of numbers (3, 2, 2, -1/2) to check if it is a possible quantum number:
1. The first number is 3. It corresponds to the principal quantum number (n). This means the electron is in the third energy level.
2. The second number is 2. It corresponds to the azimuthal quantum number (l). According to the rules, l can range from 0 to (n-1). Since n is 3, l can have values of 0, 1, or 2. So, the value of 2 is within the allowed range.
3. The third number is also 2. It corresponds to the magnetic quantum number (ml). According to the rules, ml can range from -l to +l, including zero. The value of 2 is within the allowed range for l = 2.
4. The fourth number is -1/2. It corresponds to the spin quantum number (ms). The value -1/2 is allowed for ms as it represents one of the two possible spin states of an electron.
Based on the analysis, the set of numbers (3, 2, 2, -1/2) is indeed a possible quantum number. It represents an electron in the 3rd energy level (n), in a d-subshell (l = 2), in a specific orbital (ml = 2), and with a spin downward (ms = -1/2).
If your classmates claimed it was impossible, it might be due to a misunderstanding or confusion about the rules for assigning quantum numbers.