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JEE MainChemistryStructure of Atom

An electron is present in an orbital that has 1 radial node and 2 angular nodes. Which of the following sets of quantum numbers is allowed for this electron?

Options

  1. An=3, l=2, m_l=0, s=+ 1 2
  2. Bn=4, l=2, m_l=-1, s=- 1 2
  3. Cn=4, l=1, m_l=0, s=+ 1 2
  4. Dn=4, l=2, m_l=+3, s=- 1 2

Correct answer

B. n=4, l=2, m_l=-1, s=- 1 2

Step-by-step solution

The number of angular nodes is equal to the azimuthal quantum number l . Given angular nodes = 2 , we have l = 2 . The number of radial nodes is given by the formula n - l - 1 . Given radial nodes = 1 , we have n - 2 - 1 = 1 , which gives n = 4 . For l = 2 , the allowed values of the magnetic quantum number m_l are -2, -1, 0, +1, +2 . Looking at the options, the set n=4, l=2, m_l=-1, s=- 1 2 is the only one that correctly matches these derived values and satisfies all quantum number constraints. Answer: n=4, l=2, m

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