Question

According to the Bohr's theory of hydrogen atom, the speed of the electron, energy and the radius of its orbit vary with the principal quantum number \(n\) respectively, as

• A. \(\dfrac{1}{n},\ \dfrac{1}{n^2},\ n^2\)
• B. \(\dfrac{1}{n},\ n^2,\ \dfrac{1}{n^2}\)
• C. \(n^2,\ \dfrac{1}{n^2},\ \dfrac{1}{n}\)
• D. \(n,\ \dfrac{1}{n^2},\ \dfrac{1}{n}\)

Hint:

Bohr model gives: \(r_n \propto n^2\), \(v_n \propto 1/n\), \(E_n \propto -1/n^2\). These are very common relations in MCQs.

Answer 1

The Correct Option is A

Step 1: Bohr radius relation.
Radius of nth orbit:
\[ r_n \propto n^2 \] Step 2: Velocity relation.
Electron velocity in nth orbit:
\[ v_n \propto \frac{1}{n} \] Step 3: Energy relation.
Total energy of electron:
\[ E_n \propto -\frac{1}{n^2} \] Magnitude varies as \(\dfrac{1}{n^2}\).
Step 4: Match option.
Thus variation is:
\[ \frac{1}{n},\ \frac{1}{n^2},\ n^2 \] Final Answer: \[ \boxed{\dfrac{1}{n},\ \dfrac{1}{n^2},\ n^2} \]