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JEE MainChemistryStructure of Atom

An electron is present in an orbital that has 2 radial nodes and 2 angular nodes. Which of the following sets of quantum numbers (n, l, m_l, m_s) could correctly describe this electron?

Options

  1. An=4, l=2, m_l=1, m_s=- 1 2
  2. Bn=5, l=1, m_l=-1, m_s=+ 1 2
  3. Cn=5, l=2, m_l=0, m_s=+ 1 2
  4. Dn=6, l=2, m_l=0, m_s=+ 1 2

Correct answer

C. n=5, l=2, m_l=0, m_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 = 2 , we can write: n - 2 - 1 = 2 n - 3 = 2 n = 5 The orbital is 5d . For a 5d orbital, the allowed values for the magnetic quantum number m_l are -2, -1, 0, +1, +2 . Therefore, the correct set of quantum numbers must have n=5 and l=2 . The set n=5, l=2, m_l=0, m_s=+ 1 2 satisfies these conditions. Answer: n=5, l=2, m_l=0

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