R=0.529×n^2/Z.R is directly proportional to n^2.R1/R2=n1^2/n2^2.R/R2=2^2/3^2.R/R2=4/9.R2=9R/4.R2=2.25R.

Explanation:

To understand this question, let's first discuss the concept of stationary orbits in the Bohr model of the atom.

Bohr Model of the Atom:
According to the Bohr model, electrons revolve around the nucleus of an atom in specific circular paths called stationary orbits. These orbits are characterized by their energy levels, which are quantized. The energy of an electron in a stationary orbit is given by:

E = -13.6/n^2 eV

Where E is the energy, n is the principal quantum number, and -13.6 eV is the ionization energy of hydrogen.

Relation between Radii and Energy Levels:
The radius of an orbit is directly related to the energy level of the electron. The higher the energy level, the larger the radius of the orbit. The radius of a stationary orbit is given by:

r = 0.529 Å * n^2/Z

Where r is the radius, n is the principal quantum number, and Z is the atomic number of the nucleus.

Radius of the Second Orbit:
Given that the radius of the second stationary orbit is R, we can write:

R = 0.529 Å * 2^2/Z

Radius of the Third Orbit:
To find the radius of the third orbit, we need to determine the value of n for that orbit. Since the third orbit is one level higher than the second orbit, we can write:

n = 2 + 1 = 3

Substituting this value of n into the equation for the radius of a stationary orbit, we get:

r = 0.529 Å * 3^2/Z

Comparing the Radii:
Now, let's compare the radius of the third orbit (r) with the radius of the second orbit (R):

r/R = (0.529 Å * 3^2/Z)/(0.529 Å * 2^2/Z)

Simplifying this expression, we get:

r/R = (3^2)/(2^2)

r/R = 9/4

Therefore, the ratio of the radius of the third orbit to the radius of the second orbit is 9/4.

Correct Option:
The correct option is D) 2.25R, which corresponds to a ratio of 9/4.