In Bohr model of the hydrogen atom, let R,v and E represent the radius of the orbit, speed of the electron and the total energy respectively. Which of the following quantities are directly proportional to the quantum number n?

Options

A. (i), (ii)
B. (ii), (iii)
C. (i), (iii)
D. (ii), (iv)

Answer

C

Explanation

(i) `v_(n)r_(n) prop ((Z)/(n).(n^(2))/(Z)=n) , (ii) r_(n)E_(n) prop ((n^(2))/(Z).(Z^(2))/(n^(2))=Z)`
(iii) `(v_(n))/(E_(n)) prop ((Z)/(n).(n^(2))/(n).(n^(2))/(Z^(2))=(n)/(Z)) , (iv) (r_(n))/(E_(n)) prop ((n^(2))/(Z).(n^(2))/(Z^(2))=(n^(4))/(Z^(3)))`