Question

What is the Bohr radius of a hydrogen atom?

Hint:

The Bohr radius is a fundamental constant and represents the distance between the electron and the nucleus in the hydrogen atom’s ground state.

Answer 1

Step 1: Understanding the Bohr radius.
The Bohr radius \( a_0 \) is the radius of the smallest orbit around the nucleus in a hydrogen atom. It is given by the formula: \[ a_0 = \frac{4 \pi \epsilon_0 h^2}{m_e e^2} \] where: - \( \epsilon_0 \) is the permittivity of free space, - \( h \) is Planck’s constant, - \( m_e \) is the electron mass, - \( e \) is the electron charge. Step 2: Numerical value.
The numerical value for the Bohr radius is approximately \( 0.53 \, \text{Å} \).
Step 3: Conclusion.
Thus, the Bohr radius of a hydrogen atom is \( a_0 \approx 0.53 \, \text{Å} \).