Question

What is the energy of an electron in a hydrogen atom in a stationary state corresponding to n = 2 ?

• A. \(-5.45\times 10^{-19}\) J
• B. \(-2.40\times 10^{-19}\) J
• C. \(-4.35\times 10^{-18}\) J
• D. \(-6.70\times 10^{-18}\) J

Hint:

Use E_n = -2.18e-18 J / n squared and put n = 2.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
In Bohr's model the energy of the electron in a hydrogen atom depends only on the principal quantum number \(n\). It is negative because the electron is bound to the nucleus.

Step 2: Key Formula or Approach:
\[ E_n = -\frac{2.18\times 10^{-18}}{n^2}\ \text{J} \]

Step 3: Detailed Explanation:
For \(n = 2\):
\[ E_2 = -\frac{2.18\times 10^{-18}}{4} = -5.45\times 10^{-19}\ \text{J} \]
Option (C) \(-4.35\times10^{-18}\) J is twice the ground state energy, which would need \(n\) below 1, so it is not possible. Option (D) is even larger in size than that. Option (B) does not follow from any integer \(n\) in the formula.

Step 4: Check:
The ground state energy is \(-2.18\times10^{-18}\) J, and the \(n=2\) level must lie one quarter of that value, which matches option (A).

Final Answer:
The energy at n = 2 is -5.45e-19 J. \[ \boxed{\text{(A) }-5.45\times 10^{-19}\ \text{J}} \]