Choose the correct relations on the basis of Bohr’s theory.Velocity of electron ∝ Frequency of revolution ∝ Radius of orbit ∝ n2 ZElectrostatic force on electron ∝

Sure, let's analyze the relations based on Bohr's theory step by step.

1. Velocity of electron (v) ∝: According to Bohr's theory, the velocity of an electron in the nth orbit is given by: $v_n = \frac{2 \pi k e^2 Z}{nh}$ where $k$ is Coulomb's constant, $e$ is the charge of the electron, $Z$ is the atomic number, $n$ is the principal quantum number, and $h$ is Planck's constant. From this equation, we can see that: $v_n \propto \frac{Z}{n}$

2. Frequency of revolution (f) ∝: The frequency of revolution of an electron in the nth orbit is given by: $f_n = \frac{v_n}{2 \pi r_n}$ where $r_n$ is the radius of the nth orbit. From Bohr's theory, the radius of the nth orbit is: $r_n = \frac{n^2 h^2}{4 \pi^2 k e^2 Z}$ Substituting $r_n$ and $v_n$ into the frequency equation, we get: $f_n \propto \frac{Z^2}{n^3}$

3. Radius of orbit (r) ∝: As mentioned earlier, the radius of the nth orbit is: $r_n = \frac{n^2 h^2}{4 \pi^2 k e^2 Z}$ From this equation, we can see that: $r_n \propto \frac{n^2}{Z}$

4. Electrostatic force on electron (F) ∝: The electrostatic force between the nucleus and the electron in the nth orbit is given by Coulomb's law: $F = \frac{k e^2 Z}{r_n^2}$ Substituting the expression for $r_n$ from above, we get: $F \propto \frac{Z^2}{n^4}$

So, summarizing the correct relations based on Bohr's theory:

• Velocity of electron $v \propto \frac{Z}{n}$
• Frequency of revolution $f \propto \frac{Z^2}{n^3}$
• Radius of orbit $r \propto \frac{n^2}{Z}$
• Electrostatic force on electron $F \propto \frac{Z^2}{n^4}$

These are the proportional relationships derived from Bohr's theory.