Question

The total number of allowed values of l for a given value of n is equal to _______
(a)- n
(b)- 2n + 1
(c)- 2n – 1
(d)- 2n

Answer 1

Both n and l are the quantum numbers that tell the principal quantum number and Azimuthal quantum number in which the n tells the number of the main shell, and l tells the number of the subshell. When the shell is 1, the subshell is s, when the shell is 2, then the subshells are s and p, etc, and so on.

Complete step-by-step answer: There are many elements on the earth and each element is differentiated by the number of electrons in it. Each electron in an element is defined by a set of four quantum numbers, i.e., n, l, m, and s in which n is the principal quantum number, l is the Azimuthal quantum number, m is the magnetic quantum number, and s is the spin quantum number.
The n tells the number of the main shell, and l tells the number of the subshell. Principle quantum number, i.e., n is an integer like 1, 2, 3….. The Azimuthal quantum number can be calculated by putting the value as l = 0 to l = (n – 1).
When the shell is 1, then the subshell is s. When the shell is 2, then the subshells are s and p. When the shell is 3, then the subshells are s, p, and d. When the shell is 4, then the subshells are s, p, d, and f. From this, we can say that the number of l is equal to n.

Therefore, the correct answer is an option (a)- n.

Note: When the value of l is 0, then the subshell is s. When the value of l is 1, then the subshell is p. When the value of l is 2, then the subshell is d. When the value of l is 3, then the subshell is f.