Quantum numbers arise naturally from the mathematics used to describe the possible states of an electron in an atom. the four quantum numbers, the principal quantum number (𝑛), the angular momentum quantum number (𝓁), the magnetic quantum number (𝑚_𝓁), and the spin quantum number (𝑚_s) have strict rules which govern the possible values. identify all allowable combinations of quantum numbers for an electron.

Determine whether each of the following sets of quantum numbers for the hydrogen atom are valid. If a set is not valid, indicate which of the quantum numbers has a value that is not valid: (a) n = 3, l = 3, m_l = 2, m_s = +1/2 (b) n = 4, l = 3, m_l = -3, m_s = +1/2 (c) n = 3, l = 1, m_l = 2, m_s = +1/2 (d) n = 5, l = 0, m_l = 0, m_s = 0 (e) n = 2, l = 1, m_l = 1, m_s = -1/2

Which set of three quantum numbers does not specify an orbital in the hydrogen atom?