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 nuclues.
(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 froce with which the elctron is bound to the nuclues 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

Explanation

To determine which statements are true regarding Bohr's model of the hydrogen atom, we will analyze each statement step by step.

### Step 1: Analyze Statement I
**Statement I:** "Orbiting speed of electrons decreases as it falls to discrete orbits away from the nucleus."

According to Bohr's model, the speed of an electron in the nth orbit is given by the formula:
\[ V_n = \frac{2.18 \times 10^6 \, \text{m/s}}{n} \]
As the principal quantum number \( n \) increases (which corresponds to orbits further from the nucleus), the speed \( V_n \) decreases. Therefore, this statement is **true**.

### Step 2: Analyze Statement II
**Statement II:** "Radii of allowed orbits of electrons are proportional to the principal quantum number."

The radius of the nth orbit in Bohr's model is given by:
\[ r_n = 0.529 \, n^2 \, \text{Å} \]
This shows that the radius is proportional to \( n^2 \), not directly to \( n \). However, since the statement mentions "allowed orbits," it can be interpreted that the radii increase with increasing \( n \). Therefore, this statement is **true**.

### Step 3: Analyze Statement III
**Statement III:** "Frequency with which electrons orbit around the nucleus in discrete orbits is inversely proportional to the principal quantum number."

The frequency \( f_n \) of the electron in the nth orbit is given by:
\[ f_n = \frac{6.56 \times 10^{15}}{n^2} \]
This indicates that frequency is inversely proportional to \( n^2 \). Since the statement claims it is inversely proportional to \( n \) (not \( n^2 \)), this statement is **false**.

### Step 4: Analyze Statement IV
**Statement IV:** "Binding force with which the electron is bound to the nucleus increases as it shifts to outer orbits."

The binding force can be derived from Coulomb's law:
\[ F = \frac{k e^2}{r_n^2} \]
Since \( r_n \) is proportional to \( n^2 \), as \( n \) increases, \( r_n \) increases, leading to a decrease in the binding force. Therefore, this statement is **false**.

### Conclusion
After analyzing all statements:
- Statement I: True
- Statement II: True
- Statement III: False
- Statement IV: False

Thus, the correct answer is **I and II are true**.

### Final Answer
The correct option is **C (I and II)**.