Question

According to Bohr’s Model:
(A) The radius of the orbiting electron is directly proportional to ‘n’.
(B) The speed of the orbiting electron is directly proportional to 1/n. (C) The magnitude of the total energy of the orbiting electron isdirectly proportional to 1/n².
(D) The radius of the orbiting electron is directly proportional to n².

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

Answer 1

The Correct Option is D

Analyzing the options based on Bohr's Model:

1. (A) Electron orbit radius vs. 'n':
   Bohr's model specifies electron orbit radius \( r_n \) for the nth orbit as \( r_n = n^2 \times r_1 \). This demonstrates proportionality to \( n^2 \), not \( n \). Option (A) is incorrect.
2. (B) Electron speed vs. 1/n:
   The speed \( v_n \) of the electron in the nth orbit is approximately \( v_n = \frac{v_1}{n} \), where \( v_1 \) is the speed in the first orbit. This indicates an inverse proportionality to \( n \). Option (B) is correct.
3. (C) Total electron energy magnitude vs. 1/n²:
   The total energy \( E_n \) for the nth orbit is \( E_n = \frac{-E_1}{n^2} \). This means the magnitude of the energy increases with \( 1/n^2 \). Option (C) is correct.
4. (D) Electron orbit radius vs. n²:
   As stated in point (A), the formula \( r_n = n^2 \times r_1 \) confirms direct proportionality to \( n^2 \). Option (D) is correct.

The correct options are (B), (C), and (D).