Which of the following statement is true regarding Bohr's model of hydrogen atom ?
(I) Orbiting speed of electrons decreases as if falls to discrete orbits away from the nucleus.
(II) Radii of allowed orbits of electrons are proportional to the principle quantum number.
(III) Frequency with which electrons orbit around the nucleus in discrete orbits is inversely proportional to the principle quantum number.
(IV) Binding force with which the electron is bound to the nucleus increases as it shifts to outer orbits.
Selected the correct answer using the codes given below:

Options

A. I and III
B. II and IV
C. I, II and III
D. II, III and IV

Answer

A

Explanation

Speed of electron in `n^(th)` orbit = `2.18 xx 10^6 xx Z/n`
For hydrogen atom, `Z = 1`
Speed of electron in `n^(th)` orbit for hydrogen atom = `(2.18 xx 10^6)/(n)`
So, as the value of n increases, orbiting speed of electron decreases.
Hence, I is correct.
Radii of an electron in `n^(th)` orbit = `0.529 (n^2)/Z Å`
Radii of an electron for hydrogen atom in `n^(th)` orbit = `0.529 (n^2)/(1) Å`
Radii is directly proportional to `n^2`, not to n.
Hence, II is incorrect.
Time taken by an electron to complete one revolution
`= 1.534 xx 10^(-10) xx(n^3)/(Z^2)`
T is proportional to `(n^3)/(Z^2)`
We know, frequency with which electrons orbit in nucleus `f = 1/T`
So, f is inversely proportional to `n^3` for hydrogen atom
Hence, III is correct.
Binding force with which electrons is bound to nucleus = `(KZe^2)/(r^2)`
In hydrogen atom, binding force = `(Ke^2)/(r^2)`
And, we know, as we shift to outer orbit, r increases. So, binding force decreases.
Hence, IV is incorrect.