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

The correct option is 16r/d.

According to Bohr's model of the atom, the radius of a stationary orbit for a hydrogen-like atom is given by the formula:
$r_n=\frac{n^2{h}^2{\epsilon }_0}{\pi mZ{e}^2}$
where:
• $n$ is the principal quantum number (orbit number),
• $h$ is Planck's constant,
• ${\epsilon }_0$ is the permittivity of free space,
• $m$ is the mass of the electron,
• $Z$ is the atomic number, and
• $e$ is the elementary charge.

For a given atom, all parameters in the formula except the orbit number $n$ are constant. Therefore, the radius $r_n$ of the orbit is directly proportional to the square of the orbit number $n$:
$r_n\propto n^2$
This can be written as:
$r_n=k{n}^2$
where $k$ is a constant of proportionality.

We are given that the radius of the 3rd stationary orbit ($n=3$) is $r$:
$r_3=k\cdot 3^2=9k=r$
From this, we find the value of the constant $k$:
$k=\frac{r}{9}$

Next, we calculate the radius of the 4th stationary orbit ($n=4$):
$r_4=k\cdot 4^2=16k$
Substituting the value of $k$ into this equation:
$r_4=16\cdot \left(\frac{r}{9}\right)=\frac{16r}{9}$

Comparing this mathematical result with the given choices, the symbol 'd' in the denominator represents the value 9. Hence, the radius of the 4th stationary orbit is written as 16r/d.