Consider the following sets of quantum numbers for an electron: (I) n=3, l=2, m_l=-2, m_s=+ 1 2 (II) n=4, l=4, m_l=+2, m_s=- 1 2 (III) n=5, l=1, m_l=-2, m_s=+ 1 2 (IV) n=2, l=0, m_l=0, m_s=+1 (V) n=4, l=3, m_l=0, m_s=- 1 2 How many of the above sets of quantum numbers are not permitted?

Step-by-step solution

According to the rules for quantum numbers: - Principal quantum number n can be any positive integer. - Azimuthal quantum number l can have values from 0 to (n-1) . - Magnetic quantum number m_l can have values from -l to +l . - Spin quantum number m_s can only be + 1 2 or - 1 2 . Evaluating the given sets: (I) Permitted. Represents an electron in a 3d orbital. (II) Not permitted because l cannot be equal to n . For n=4 , the maximum value of l is 3 . (III) Not permitted because m_l cannot be -2 when l=1 . The allo