Excited hydrogen atoms with very large radii have been detected. How large is an H atom with an electron characterised by a quantum number of 106? How many times larger is that than the radius of an H atom in its ground state?

Explanation

To solve the question, we will use the formula for the radius of a hydrogen atom in a given quantum state:

\[ R_n = \frac{n^2}{Z} \times 0.529 \, \text{Å} \]

where:
- \( R_n \) is the radius of the hydrogen atom in the \( n \)th quantum state,
- \( n \) is the principal quantum number,
- \( Z \) is the atomic number (for hydrogen, \( Z = 1 \)),
...