Question

When hydrogen atom is in its first excited level, its radius, is

• A. twice
• B. half
• C. same
• D. four times

Answer 1

The Correct Option is D

To determine the radius of a hydrogen atom when it is in its first excited state, we need to explore the Bohr model of the hydrogen atom. The Bohr model introduces the concept of quantized orbits for electrons, where each orbit corresponds to a certain energy level characterized by the principal quantum number \( n \).

According to the Bohr model, the radius of the electron orbit in a hydrogen atom is given by the formula:

r_n = n^2 \cdot a_0

• r_n is the radius of the orbit corresponding to the principal quantum number n.
• a_0 is the Bohr radius, which is approximately \(0.529 \, \text{Å}\).
• n is the principal quantum number, representing the energy level.

For the ground state of the hydrogen atom, n = 1, and thus the radius is:

r_1 = 1^2 \cdot a_0 = a_0

When the hydrogen atom is in its first excited state, the principal quantum number becomes n = 2. Applying the formula, the radius is:

r_2 = 2^2 \cdot a_0 = 4a_0

Therefore, when the hydrogen atom is in its first excited level, its radius is four times that of the ground state.

Thus, the correct answer is four times.