The following sets of quantum numbers are not valid but can be made so by correcting one value

Oct 13, 2025 by windailys.com 110 views

The following sets of quantum numbers are not valid but can be made so by correcting one value

Quantum numbers are a set of four numbers that describe the energy, shape, and orientation of an electron's orbital in an atom. These numbers are denoted as n, l, m_l, and m_s. The first three numbers, n, l, and m_l, describe the orbital, while the fourth number, m_s, describes the spin of the electron. In this article, we will discuss the sets of quantum numbers that are not valid but can be made so by correcting one value.

Sets of Quantum Numbers with Invalid Values

Set 1: n = 1, l = 2, m_l = -1, m_s = -1/2

In this set, the value of l is invalid. The value of l can range from 0 to n-1. Since n = 1, the maximum value of l is 0. Therefore, the value of l should be corrected to 0.

Set 2: n = 2, l = 1, m_l = 2, m_s = -1/2

In this set, the value of m_l is invalid. The value of m_l can range from -l to +l. Since l = 1, the maximum value of m_l is 1. Therefore, the value of m_l should be corrected to 1.

Set 3: n = 3, l = 2, m_l = -2, m_s = 1/2

In this set, the value of m_l is invalid. The value of m_l can range from -l to +l. Since l = 2, the maximum value of m_l is 2. Therefore, the value of m_l should be corrected to 2.

Set 4: n = 4, l = 0, m_l = 0, m_s = -1/2

In this set, the value of m_s is invalid. The value of m_s can be either +1/2 or -1/2. Since m_s = -1/2, it is a valid value. However, the value of m_l is also invalid. The value of m_l can range from -l to +l. Since l = 0, the value of m_l should be corrected to 0.

Set 5: n = 5, l = 3, m_l = -3, m_s = 1/2

In this set, the value of m_l is invalid. The value of m_l can range from -l to +l. Since l = 3, the maximum value of m_l is 3. Therefore, the value of m_l should be corrected to 3.

Set 6: n = 6, l = 2, m_l = 0, m_s = -1/2

Set 7: n = 7, l = 1, m_l = -1, m_s = 1/2

In this set, the value of m_s is invalid. The value of m_s can be either +1/2 or -1/2. Since m_s = 1/2, it is a valid value. However, the value of m_l is also invalid. The value of m_l can range from -l to +l. Since l = 1, the maximum value of m_l is 1. Therefore, the value of m_l should be corrected to 1.

Set 8: n = 8, l = 3, m_l = 0, m_s = -1/2

Set 9: n = 9, l = 2, m_l = 2, m_s = 1/2

In this set, the value of m_l is invalid. The value of m_l can range from -l to +l. Since l = 2, the maximum value of m_l is 2. Therefore, the value of m_l should be corrected to 2.

Set 10: n = 10, l = 0, m_l = 0, m_s = 1/2

Conclusion

In conclusion, the sets of quantum numbers that are not valid but can be made so by correcting one value are:

Set 1: n = 1, l = 2, m_l = -1, m_s = -1/2 (l = 0)
Set 2: n = 2, l = 1, m_l = 2, m_s = -1/2 (m_l = 1)
Set 3: n = 3, l = 2, m_l = -2, m_s = 1/2 (m_l = 2)
Set 4: n = 4, l = 0, m_l = 0, m_s = -1/2 (m_l = 0)
Set 5: n = 5, l = 3, m_l = -3, m_s = 1/2 (m_l = 3)
Set 6: n = 6, l = 2, m_l = 0, m_s = -1/2 (m_l = 2)
Set 7: n = 7, l = 1, m_l = -1, m_s = 1/2 (m_l = 1)
Set 8: n = 8, l = 3, m_l = 0, m_s = -1/2 (m_l = 3)
Set 9: n = 9, l = 2, m_l = 2, m_s = 1/2 (m_l = 2)
Set 10: n = 10, l = 0, m_l = 0, m_s = 1/2 (m_l = 0)

By correcting the invalid values, we can obtain valid sets of quantum numbers.