It is given that radius of 3rd stationary orbit is r, find out radius of 4th stationary orbit.

The correct option is 16r/d (where the denominator d represents 9 due to a typographical variation in the options, corresponding to the derived value of $\frac{16r}{9}$).

Step-by-Step Derivation:

According to Bohr's model of the hydrogen atom (and hydrogen-like species), the radius $r_n$ of the $n^{\text{th}}$ stationary orbit is given by the relation:
$$r_n\propto \frac{n^2}{Z}$$
where $n$ is the principal quantum number (orbit number) and $Z$ is the atomic number.
For a given atom, $Z$ is constant, so we can write:
$$r_n=K{n}^2$$
where $K$ is a constant of proportionality.

Step 1: Express the radius of the 3rd orbit ($n=3$)
The radius of the 3rd stationary orbit is given as $r$. Substituting $n=3$ into our relation:
$$r=K{3}^2=9K$$
Solving for the constant $K$:
$$K=\frac{r}{9}$$

Step 2: Find the radius of the 4th orbit ($n=4$)
Now, we calculate the radius $r_4$ for $n=4$:
$$r_4=K{4}^2=16K$$
Substitute the expression for $K$ from Step 1:
$$r_4=16\left(\frac{r}{9}\right)=\frac{16r}{9}$$

Comparing our result with the options, the variable $d$ in the denominator of the correct answer 16r/d represents the value $9$.