bohr radius

Question

Bohr radius a0 approximately equals?

RankGuru · Accepted Answer

1. **Definition**: The Bohr radius ($a_0$) is the most probable distance between the nucleus and the electron in a hydrogen atom in its ground state ($n=1$).
2. **Formula**: Derived from electrostatics and quantization of angular momentum:
   $r_n = \frac{\epsilon_0 h^2 n^2}{\pi m e^2 Z} = a_0 \frac{n^2}{Z}$
3. **Constant Value**: Substituting fundamental constants:
   $a_0 = \frac{\epsilon_0 h^2}{\pi m e^2} \approx 0.529 	imes 10^{-10} 	ext{ m}$
4. **Conversion**: Since $1 	ext{ \AA} = 10^{-10} 	ext{ m}$, the Bohr radius is **0.529 \AA**.

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Bohr radius a_0 for hydrogen represents: