High School

Which of the following statements is invalid?

A) \( m \cdot n \cdot q = 3500 \)

B) \( m \cdot n \cdot q = 3500, 3600, 3700 \)

C) \( m, n, q = 3500, 3600, 3700 \)

D) \( m \cdot n \cdot q = 350036003700 \)

Answer :

Final answer:

Assuming standard mathematical notation, statement b) 'm.n.q=3500,3600,3700' is invalid as it suggests a single set of variables has multiple different products simultaneously, which is not mathematically standard.

Explanation:

The student's question pertains to the validity of given statements which seem to refer to quantum numbers. Quantum numbers include the principal quantum number (n), azimuthal quantum number (l), magnetic quantum number (mê), and spin quantum number (ms). These can only have certain discrete values that are used to describe the properties of an electron in an atom. For a set of quantum numbers to be considered valid, they must adhere to specific rules:

  • The principal quantum number (n) must be a positive integer.
  • The azimuthal quantum number (l) is an integer from 0 to n - 1.
  • The magnetic quantum number (mê) can range from -l to +l.
  • The spin quantum number (ms) can only be +1/2 or -1/2.

Given this information, we can examine the options:

  1. {3, 2, 1, +1/2} is a valid set of quantum numbers.
  2. {2, 2, 0, -1/2} is not a valid set because l cannot be equal to n.
  3. {3, −1, 0, +1/2} is not a valid set because l must be a non-negative integer.

Looking at the student's statements:

  • a) 'm.n.q=3500' is hard to assess without context but is a simple numerical equality.
  • b) 'm.n.q=3500,3600,3700' suggests multiple values for a single product which is not mathematically standard.
  • c) 'm,n,q=3500,3600,3700' seems to imply a list of variables equaling various values which could be valid if these are simply representing different variables taking on different values.
  • d) 'mnq=350036003700' looks like a concatenation of numbers rather than an expression of an operation between variables.

Assuming typical mathematical notation is being used, statement b) 'm.n.q=3500,3600,3700' would be considered invalid as it suggests a single set of variables has multiple different products simultaneously which is not possible. However, for quantum numbers, the list of numerical values would also be invalid if they are intended to represent quantum numbers, as they would violate the discrete and specific nature of these numbers.

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