Chapter 26. Magnitude of the angular momentum of a particle (8-23)

Question

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Question

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{"title":"Magnitude of the angular momentum of a particle","description":"Wrong","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"10,16,12,16\"},{\"shape\":\"poly\",\"coords\":\"144,22\"},{\"shape\":\"rect\",\"coords\":\"1,3,24,35\"}]"} {"title":"Component of the particle’s linear momentum perpendicular to the vector r from rotation axis to particle","description":"Correct!","type":"correct","color":"#ffff00","code":"[{\"shape\":\"rect\",\"coords\":\"105,9,128,41\"},{\"shape\":\"rect\",\"coords\":\"228,6,273,37\"}]"} {"title":"Distance from the rotation axis to the particle","description":"Incorrect","type":"incorrect","color":"#00ff00","code":"[{\"shape\":\"rect\",\"coords\":\"89,10,107,35\"},{\"shape\":\"rect\",\"coords\":\"182,12,201,37\"}]"}

Question

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{"title":"Magnitude of the angular momentum of a particle","description":"Wrong","type":"incorrect","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"10,16,12,16\"},{\"shape\":\"poly\",\"coords\":\"144,22\"},{\"shape\":\"rect\",\"coords\":\"1,3,24,35\"}]"} {"title":"Component of the particle’s linear momentum perpendicular to the vector r from rotation axis to particle","description":"Incorrect","type":"incorrect","color":"#ffff00","code":"[{\"shape\":\"rect\",\"coords\":\"105,9,128,41\"},{\"shape\":\"rect\",\"coords\":\"228,6,273,37\"}]"} {"title":"Distance from the rotation axis to the particle","description":"Correct!","type":"correct","color":"#00ff00","code":"[{\"shape\":\"rect\",\"coords\":\"89,10,107,35\"},{\"shape\":\"rect\",\"coords\":\"182,12,201,37\"}]"}

Review

To relate angular momentum to Equation 26-18, we express \(L\) in terms of the mass of the electron \(m_{\mathrm{e}}\), its speed \(v\), and its distance from the center of the atom \(r\) using Equation 8-23:

Since the electron moves in a circle, the vector from the rotation axis to the particle always has the same radius \(r\) and is always perpendicular to the momentum vector.