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AP Physics 2
15.2 The Bohr Model of Atomic Structure
AdvancedMCQMathematical17.8k
A circular path with a thin black outline represents an electron orbit centered on a small filled circle labeled with a plus sign representing a proton. On the top of the circular path, a small open circle represents an electron. A dashed line segment extends radially from the central proton to the electron, labeled r_n for the orbit radius. An arrow labeled \vec{F}_e originates at the electron and points radially inward toward the proton. A second arrow labeled \vec{v}_n originates at the electron and points horizontally to the left, perpendicular to the radial dashed line. No other labels, lines, text, or axes appear.
Electron in a circular Bohr orbit around a proton.
In the Bohr model of the hydrogen atom, an electron of mass \(m_e\) and charge magnitude \(e\) moves in a circular orbit of radius \(r_n\) around a stationary proton. The electrostatic force provides the centripetal acceleration, and the electron's orbital angular momentum is quantized according to \(m_e v_n r_n = \dfrac{n h}{2\pi}\), where \(n\) is a positive integer and \(h\) is Planck's constant. Which of the following expressions correctly represents the speed \(v_n\) of the electron in the \(n\text{th}\) orbit in terms of \(n\), \(h\), \(e\), Coulomb's constant \(k\), and fundamental constants?

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