Give the relationship between orbital radius and velocity of an electron for a hydrogen atom.
(N/A) According to Bohr's theory of the hydrogen atom,the electrostatic force between the nucleus and the electron provides the necessary centripetal force for circular motion:
$F_e = F_c$
$\frac{1}{4\pi\epsilon_0} \cdot \frac{e^2}{r^2} = \frac{mv^2}{r}$
From this,we can derive the relationship between the orbital radius $r$ and the velocity $v$ of the electron:
$\frac{1}{4\pi\epsilon_0} \cdot \frac{e^2}{r} = mv^2$
Thus,the relationship is $r = \frac{e^2}{4\pi\epsilon_0 mv^2}$.
$F_e = F_c$
$\frac{1}{4\pi\epsilon_0} \cdot \frac{e^2}{r^2} = \frac{mv^2}{r}$
From this,we can derive the relationship between the orbital radius $r$ and the velocity $v$ of the electron:
$\frac{1}{4\pi\epsilon_0} \cdot \frac{e^2}{r} = mv^2$
Thus,the relationship is $r = \frac{e^2}{4\pi\epsilon_0 mv^2}$.
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