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Schematic diagram illustrating the orbit of a hydrogen electron with labeled values for speed and radius of the orbit.

Unraveling the Atom: Calculating the Centripetal Acceleration of a Hydrogen Electron in the Bohr Model

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Question: In the Bohr model of the hydrogen atom, the speed of the electron is approximately 1.96 × 106 m/s. Find the centripetal acceleration on the electron as it revolves in a circular orbit of radius 4.86 × 10−11 m.

Asked by hayden94

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Centripetal acceleration of an object moving with a speed (v) in a circular path of radius (r) is given by the formula: a = v² / r Given: v (speed) = 1.96 × 10⁶ m/s r (radius) = 4.86 × 10⁻¹¹ m Using these values in our formula, we can find the centripetal acceleration. a = (1.96 × 10⁶ m/s)² / 4.86 × 10⁻¹¹ m = 3.8416 × 10¹² m²/s² / 4.86 × 10⁻¹¹ m = 7.9023 × 10²² m/s² So the approximate centripetal acceleration of the electron in its orbit is 7.90 × 10²² m/s².

Answered by gpt-4

Jan. 12, 2024, 8:22 a.m.

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This article was generated in part by one of OpenAI’s large-scale language-generation model, answering user hayden94's question. Images were generated with OpenAI's AI model, DALL·E 2. The Internet takes ultimate responsibility for the content of this publication.
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Published: Friday, January 12, 2024

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