Question

Bohr’s radius of H-atom is \( 2.12 \times 10^{-10} \) m. Calculate the energy of electron at this level.

• A. \( -5.44 \times 10^{-19} \) J
• B. \( -2.176 \times 10^{-18} \) J
• C. \( -54.4 \times 10^{-19} \) J
• D. \( -2.3 \times 10^{-19} \) J

Hint:

In Bohr’s model, the energy of the electron is quantized and is inversely proportional to the square of the principal quantum number.

Answer 1

The Correct Option is A

Step 1: Formula for energy of electron in Bohr’s model.
The energy of an electron in a hydrogen atom according to Bohr’s model is given by: \[ E = - \frac{13.6 \, \text{eV}}{n^2} \] where \( n \) is the principal quantum number. For the first energy level (\( n = 1 \)): \[ E = -13.6 \, \text{eV} \] Step 2: Convert energy to joules.
1 eV = \( 1.602 \times 10^{-19} \) J, so: \[ E = -13.6 \times 1.602 \times 10^{-19} \, \text{J} = -5.44 \times 10^{-19} \, \text{J} \] Step 3: Conclusion.
Thus, the energy of the electron is \( -5.44 \times 10^{-19} \, \text{J} \). Final Answer: \[ \boxed{-5.44 \times 10^{-19} \, \text{J}} \]