Give the maximum number of electrons in an atom that can have the following set of quantum numbers.
(a) n=4
(b) n = 5, ml = 1,
(c) n = 5, ms = 1/2
A 32
B 8
C 2
To find the maximum number of electrons in an atom with a given set of quantum numbers, we need to use the following rules:
1. The principal quantum number (n) describes the energy level or shell of the electron. The maximum number of electrons in a shell is given by the formula 2n^2.
2. The magnetic quantum number (ml) describes the orientation of the electron's orbital within a given subshell. The range of values for ml is from -l to +l, where l is the azimuthal quantum number. For a given n, the maximum value of ml is (n-1).
3. The spin quantum number (ms) describes the direction of the electron's spin. It can have two values: +1/2 (spin-up) or -1/2 (spin-down).
Now let's apply these rules to each set of quantum numbers:
(a) For n = 4:
The maximum number of electrons in the fourth shell is given by 2n^2 = 2 * 4^2 = 32. Therefore, the maximum number of electrons is 32.
(b) For n = 5 and ml = 1:
The maximum value of ml for n = 5 is (5-1) = 4. Therefore, there are 2 * 4 + 1 = 9 possible orientations for ml. Each orientation can have two electrons (due to the spin), so the maximum number of electrons is 9 * 2 = 18.
(c) For n = 5 and ms = 1/2:
The value of ms does not affect the maximum number of electrons. The maximum number of electrons is still determined by the principal quantum number (n). Therefore, the maximum number of electrons is 2 * 5^2 = 50.
In summary:
(a) The maximum number of electrons is 32.
(b) The maximum number of electrons is 18.
(c) The maximum number of electrons is 50.