Question

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

• A. $-1.45 \times 10^{-18}\ \text{J}$
• B. $-0.545 \times 10^{-18}\ \text{J}$
• C. $-3.45 \times 10^{-18}\ \text{J}$
• D. $-2.5 \times 10^{-18}\ \text{J}$

Hint:

If you already remember the standard energy values in electron-volts, the calculation is even faster: $E_2 = -3.4\ \text{eV}$. Multiplying by the conversion factor ($1.6 \times 10^{-19}\ \text{J/eV}$) gives: $-3.4 \times 1.6 \times 10^{-19} = -5.44 \times 10^{-19}\ \text{J} = -0.544 \times 10^{-18}\ \text{J}$.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
We need to calculate the total energy (in Joules) of an electron residing in the second stationary Bohr orbit (n = 2) of a hydrogen atom.

Step 2: Key Formula or Approach:
According to Bohr's model, the energy of an electron in the n-th orbit is given by E_n = –(2.18 × 10⁻¹⁸) / n² J.

Step 3: Detailed Explanation:
For n = 2, we substitute into the formula: E₂ = –(2.18 × 10⁻¹⁸) / 2² = –(2.18 × 10⁻¹⁸) / 4 = –0.545 × 10⁻¹⁸ J.

Step 4: Final Answer:
The energy is –0.545 × 10⁻¹⁸ J, matching option (B).