Atomic Structure

Step 1: Understanding Ground State Energy Formula
The ground state energy ( ) of a hydrogen-like ion is given by the formula: where: - is the atomic number, - is the principal quantum number (for ground state, ).

Step 2: Calculating for Each Ion
- For Hydrogen ( ), : - For Helium ion ( ), : - For Lithium ion ( ), :

Step 3: Finding the Ratio

For a 4d orbital:
The angular nodes for is . The radial nodes are given by , so for and , the radial nodes are . Thus, the total number of nodes is .