Question

According to Bohr's atomic theory : (A) Kinetic energy of electron is $\propto Z^2 / n^2$. (B) The product of velocity (v) of electron and principal quantum number (n), 'vn' $\propto Z^2$. (C) Frequency of revolution of electron in an orbit is $\propto Z^2 / n^3$. (D) Coulombic force of attraction on the electron is $\propto Z^3 / n^4$. Choose the most appropriate answer :

• A. (A), (C) and (D) only
• B. (A) and (D) only
• C. (C) only
• D. (A) only

Hint:

Remember the core proportionalities: $r \propto n^2/Z$, $v \propto Z/n$, and $E \propto Z^2/n^2$. Most other properties like force, frequency, and momentum can be derived from these three.

Answer 1

The Correct Option is B

Step 1: Kinetic Energy $K.E. = -Total\ Energy \propto \frac{Z^2}{n^2}$. So (A) is correct.
Step 2: Velocity $v \propto \frac{Z}{n}$. Therefore, $vn \propto Z$. Statement (B) is incorrect.
Step 3: Frequency $f = \frac{v}{2\pi r}$. Since $v \propto \frac{Z}{n}$ and $r \propto \frac{n^2}{Z}$, $f \propto \frac{Z/n}{n^2/Z} \propto \frac{Z^2}{n^3}$. Statement (C) is incorrect (prompt says $Z^3$).
Step 4: Coulombic Force $F = \frac{kZe^2}{r^2}$. Since $r \propto \frac{n^2}{Z}$, $F \propto \frac{Z}{(n^2/Z)^2} \propto \frac{Z^3}{n^4}$. Statement (D) is correct.