Answer
The uncertainty in the electron’s position is comparable to the Bohr radius.
Work Step by Step
The electron is in the ground state. To find the momentum, use equation 27–11, Bohr’s quantum condition for the hydrogen atom.
$$mvr_n=n\hbar$$
$$mv=p=\frac{n\hbar}{r_n}$$
We assume that the uncertainty in p is comparable to p itself. For the ground state, n = 1.
$$\Delta p = \frac{\hbar}{r_1}$$
Apply the uncertainty principle.
$$\Delta x \Delta p \approx \hbar$$
$$\Delta x \approx \frac{\hbar}{\Delta p}=\frac{\hbar}{\hbar/r_1}=r_1$$
The uncertainty in the electron’s position is comparable to the Bohr radius.
