Which of the following is the correct ground-state electron configuration for an atom with 104 electrons?

• A. Xe 4f^{14} 5d^{10} 6s^{2} 6p^{4}
• B. Rn 5f^{14} 6d^{2} 7s^{2}
• C. Xe 4f^{14} 5d^{10} 6s^{2} 6p^{6}
• D. Rn 5f^{14} 6d^{10} 7s^{2}

Answer: (B)

Verified step by step guidance

1. Step 1: Identify the element with 104 electrons. Since the atomic number equals the number of electrons in a neutral atom, the element with 104 electrons is Rutherfordium (Rf), which has atomic number 104.
2. Step 2: Recall the order of electron filling based on the Aufbau principle, which states that electrons fill orbitals starting from the lowest energy level to higher ones. For heavy elements, the filling order includes the 5f, 6d, and 7s orbitals after the noble gas radon (Rn).
3. Step 3: Write the electron configuration starting from the noble gas core Rn (which accounts for 86 electrons), then add the electrons in the 5f, 6d, and 7s orbitals to reach a total of 104 electrons.
4. Step 4: Remember that the 5f orbitals fill with 14 electrons, the 6d orbitals fill next, and the 7s orbitals fill with 2 electrons. For element 104, the 5f orbitals are fully filled (14 electrons), the 6d orbitals have 2 electrons, and the 7s orbitals have 2 electrons.
5. Step 5: Combine these to write the full ground-state electron configuration as \(\mathrm{Rn}\ 5f^{14}\ 6d^{2}\ 7s^{2}\), which corresponds to the correct configuration for an atom with 104 electrons.