Question

From their location in the diagram, what are two possible values for n and m?

A diagram with concentric circles. The outer circle is labeled rational numbers, with an m. The middle circle is labeled integers. The smallest is labeled whole numbers, with an n.

m=3.3, n=−14

m=−2, n=−62

m=6, n=−43

m=−38, n=12

Answer 1

The values for n and m must respectively fit the categories of whole numbers and rational numbers. m=3.3 is a rational number and n=12 is a whole number, making these the correct possible values.

Step-by-step explanation:

The student is asking about the possible values for n (principal quantum number) and m (magnetic quantum number) within different number sets. Since the diagram shows concentric circles with the innermost labeled as whole numbers, the value of n must be a non-negative integer. Consequently, negative values for n, such as -14, -43, or -62, are not possible because whole numbers range from 0 to positive infinity. Regarding m, which is within the outer circle labeled rational numbers, m can be any number that can be written as a fraction (including integers and decimals like 3.3), except that it cannot be a non-integer within the integers or whole numbers circles.

Therefore, acceptable values from the options given would be m=3.3, because it is a rational number, and n=12, since it is a non-negative integer and hence a whole number.