(7) [10 points] The Bohr radius is the characteristic size of a hydrogen atom, which can be expressed by a combination of fundamental constants. Choose the correct expression for the Bohr radius. Here, $\hbar$ is the reduced Planck constant, k is the Coulomb constant, $m_{e}$ is the electron mass, $e$ is the electron charge, and $G$ is the gravitational constant.

(A) $\frac{\hbar^{2}}{km_{e}e^{2}}$

(B) $\frac{G\hbar^{2}m_{e}}{k^{2}e^{2}}$

(C) $\frac{\hbar^{2}}{Gm_{e}^{3}e^{2}}$

(D) $\frac{\hbar^{2}}{m_{e}^{2}e^{2}\sqrt{Gk}}$

(E) $\sqrt{\frac{\hbar^{2}}{Gm_{e}e^{2}}}$

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