In Bohr's model of the hydrogen atom, the radius of the n^ th stationary orbit of the electron is R . If the radius of the first stationary orbit is R 25 , then the value of n is:

Step-by-step solution

According to Bohr's atomic model, the radius of the n^ th stationary orbit is proportional to the square of the principal quantum number n . r_n = r₁ n^2 Given that r_n = R and r₁ = R 25 , we can substitute these values into the relation: R = ( R 25 ) n^2 n^2 = 25 n = 5 Thus, the principal quantum number n is 5. Answer: 5