Which of the following statement(s) is/are true ? A. If two orbitals have the same value of (n + l), the orbital with lower value of n will have lower energy. B. Energies of the orbitals in the same subshell increase with increase in atomic number. C. The size of 2p_x orbital is less than the size of 3p_x orbital. D. Among 5f, 6s, 4d, 5p and 5d orbitals, none of the orbitals have 2 radial nodes. Choose the correct answer from the options given below :
B. A and C only
Statement A: According to the (n+l) rule, if two orbitals have the same (n+l) value, the orbital with the lower value of n has lower energy. This statement is true. Statement B: As the atomic number increases, the effective nuclear charge (Z_ eff ) increases. The energy of an orbital is proportional to - Z_ eff ^2 n^2 . Thus, the energy becomes more negative, meaning the energy of the orbitals in the same subshell decreases with an increase in atomic number. This statement is false. Statement C: The size of an orbital increases with an increase in the principal quantum number n. Therefore, the size of the 2p_x orbital is less than the size of the 3p_x orbital. This statement is true. Statement D: The number of radial nodes is given by the formula n - l - 1. For 5f: 5 - 3 - 1 = 1 For 6s: 6 - 0 - 1 = 5 For 4d: 4 - 2 - 1 = 1 For 5p: 5 - 1 - 1 = 3 For 5d: 5 - 2 - 1 = 2 Since the 5d orbital has exactly 2 radial nodes, the statement that none of the orbitals have 2 radial nodes is false. Therefore, only statements A and C are true. Answer: A and C only
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