Calculate the radius of Bohr's fifth orbit for hydrogen atom. Also calculate the radius of third orbit of `He^(+)` ion

Explanation

To solve the problem of calculating the radius of Bohr's fifth orbit for a hydrogen atom and the radius of the third orbit of the He\(^+\) ion, we will use the formula for the radius of an orbit in the Bohr model of the atom.

### Step 1: Calculate the radius of the fifth orbit for hydrogen atom (H)

The formula for the radius of the \(n\)th orbit in a hydrogen atom is given by:

\[
r_n = n^2 \cdot \frac{a_0}{Z}
...