Which level of the doubly ionized lithium has the same energy as the ground state energy of the hydrogen atom? Compare the orbital radii of the two levels.
Text Solution
AI Generated Solution
To solve the problem, we need to find the level of the doubly ionized lithium atom (Li²⁺) that has the same energy as the ground state energy of the hydrogen atom (H). We will also compare the orbital radii of these two levels.
### Step 1: Understand the energy levels of hydrogen and Li²⁺
The energy levels of a hydrogen-like atom can be expressed as:
\[ E_n = E_1 \cdot \frac{Z^2}{n^2} \]
where:
- \( E_n \) is the energy of the nth level,
- \( E_1 \) is the ground state energy,
...
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