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

According to Bohr's Model, let's examine each of the given options:

1. (A) The radius of the orbiting electron is directly proportional to ‘n’:
   In Bohr's model, the radius \( r_n \) of the nth orbit is given by the formula: \( r_n = n^2 \times r_1 \). This shows that the radius is proportional to \( n^2 \), not \( n \) itself. Hence, (A) is incorrect.
2. (B) The speed of the orbiting electron is directly proportional to 1/n:
   The speed \( v_n \) of the electron in the nth orbit can be approximated using the formula: \( v_n = \frac{v_1}{n} \), where \( v_1 \) is the speed in the first orbit. Therefore, the speed is indeed inversely proportional to \( n \). Thus, (B) is correct.
3. (C) The magnitude of the total energy of the orbiting electron is directly proportional to 1/n²:
   The total energy \( E_n \) of the nth orbit is given by: \( E_n = \frac{-E_1}{n^2} \), implying that energy magnitude increases with \( 1/n^2 \). Hence, (C) is correct.
4. (D) The radius of the orbiting electron is directly proportional to n²:
   As noted in point (A), the formula \( r_n = n^2 \times r_1 \) clearly shows direct proportionality to \( n^2 \). Therefore, (D) is correct.

So, the correct answer is (D): (B), (C), and (D) only.

 

Answer 2

Let's analyze each statement based on Bohr's model.

(A) The radius of the orbiting electron is directly proportional to ‘n’.

According to Bohr's model, the radius (r) of the nth orbit is given by:

r = n²h²ε₀ / (πme²Z)

Where:

• n is the principal quantum number
• h is Planck's constant
• ε₀ is the permittivity of free space
• m is the mass of the electron
• e is the charge of the electron
• Z is the atomic number

Therefore, r ∝ n², not n. So (A) is incorrect.

(B) The speed of the orbiting electron is directly proportional to 1/n.

The speed (v) of the electron in the nth orbit is given by:

v = e²Z / (2ε₀nh)

Therefore, v ∝ 1/n. So (B) is correct.

(C) The magnitude of the total energy of the orbiting electron is directly proportional to 1/n².

The total energy (E) of the electron in the nth orbit is given by:

E = -me⁴Z² / (8ε₀²h²n²)

Therefore, |E| ∝ 1/n². So (C) is correct.

(D) The radius of the orbiting electron is directly proportional to n².

As mentioned in (A), r ∝ n². So (D) is correct.

Therefore, the correct statements are (B), (C), and (D).

The correct answer is:

Option 4: (B), (C), and (D) only