Chapter 26. Bohr radius (26-22)

Question

pb0xphnT/b00WcHFaYlwdQ==
{"title":"Bohr radius","description":"Correct!","type":"correct","color":"#99CCFF","code":"[{\"shape\":\"poly\",\"coords\":\"82,133\"},{\"shape\":\"rect\",\"coords\":\"10,16,12,16\"},{\"shape\":\"poly\",\"coords\":\"144,22\"},{\"shape\":\"rect\",\"coords\":\"1,69,26,100\"}]"} {"title":"Planck’s constant divided by 2 pi","description":"Incorrect","type":"incorrect","color":"#ffff00","code":"[{\"shape\":\"rect\",\"coords\":\"173,20,204,70\"}]"} {"title":"Magnitude of the electron charge","description":"Incorrect","type":"incorrect","color":"#00ff00","code":"[{\"shape\":\"rect\",\"coords\":\"217,108,243,141\"}]"} {"title":"Coulomb constant","description":"Incorrect","type":"incorrect","color":"#ff0000","code":"[{\"shape\":\"rect\",\"coords\":\"182,90,213,143\"}]"} {"title":"Mass of the electron","description":"Incorrect","type":"incorrect","color":"#000000","code":"[{\"shape\":\"rect\",\"coords\":\"114,104,163,140\"}]"}

Question

5LnaFvF6rcbswc3/Il5BBSl5d+ZS3UvJlqyrQUHQ0Of8QtGa5rw0XwD6+JU=
{"title":"Bohr radius","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\":\"1,69,26,100\"}]"} {"title":"Planck’s constant divided by 2 pi","description":"Correct!","type":"correct","color":"#ffff00","code":"[{\"shape\":\"rect\",\"coords\":\"173,20,204,70\"}]"} {"title":"Magnitude of the electron charge","description":"Incorrect","type":"incorrect","color":"#00ff00","code":"[{\"shape\":\"rect\",\"coords\":\"217,108,243,141\"}]"} {"title":"Coulomb constant","description":"Incorrect","type":"incorrect","color":"#ff0000","code":"[{\"shape\":\"rect\",\"coords\":\"182,90,213,143\"}]"} {"title":"Mass of the electron","description":"Incorrect","type":"incorrect","color":"#000000","code":"[{\"shape\":\"rect\",\"coords\":\"114,104,163,140\"}]"}

Question

QFZ7l24zFPdEXlHLZnZ8qWs2I/MV8CKQKBQIvTtQPcGyt8Uy
{"title":"Bohr radius","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\":\"1,69,26,100\"}]"} {"title":"Planck’s constant divided by 2 pi","description":"Incorrect","type":"incorrect","color":"#ffff00","code":"[{\"shape\":\"rect\",\"coords\":\"173,20,204,70\"}]"} {"title":"Magnitude of the electron charge","description":"Correct!","type":"correct","color":"#00ff00","code":"[{\"shape\":\"rect\",\"coords\":\"217,108,243,141\"}]"} {"title":"Coulomb constant","description":"Incorrect","type":"incorrect","color":"#ff0000","code":"[{\"shape\":\"rect\",\"coords\":\"182,90,213,143\"}]"} {"title":"Mass of the electron","description":"Incorrect","type":"incorrect","color":"#000000","code":"[{\"shape\":\"rect\",\"coords\":\"114,104,163,140\"}]"}

Question

qa1mk10p/iS1MNFdqOxPC0MZHBc=
{"title":"Bohr radius","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\":\"1,69,26,100\"}]"} {"title":"Planck’s constant divided by 2 pi","description":"Incorrect","type":"incorrect","color":"#ffff00","code":"[{\"shape\":\"rect\",\"coords\":\"173,20,204,70\"}]"} {"title":"Magnitude of the electron charge","description":"Wrong","type":"incorrect","color":"#00ff00","code":"[{\"shape\":\"rect\",\"coords\":\"217,108,243,141\"}]"} {"title":"Coulomb constant","description":"Correct!","type":"correct","color":"#ff0000","code":"[{\"shape\":\"rect\",\"coords\":\"182,90,213,143\"}]"} {"title":"Mass of the electron","description":"Incorrect","type":"incorrect","color":"#000000","code":"[{\"shape\":\"rect\",\"coords\":\"114,104,163,140\"}]"}

Question

RAAqrSMq+tKpiXvnFhIgU7cYL2Qsfjf2
{"title":"Bohr radius","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\":\"1,69,26,100\"}]"} {"title":"Planck’s constant divided by 2 pi","description":"Incorrect","type":"incorrect","color":"#ffff00","code":"[{\"shape\":\"rect\",\"coords\":\"173,20,204,70\"}]"} {"title":"Magnitude of the electron charge","description":"Wrong","type":"incorrect","color":"#00ff00","code":"[{\"shape\":\"rect\",\"coords\":\"217,108,243,141\"}]"} {"title":"Coulomb constant","description":"Wrong","type":"incorrect","color":"#ff0000","code":"[{\"shape\":\"rect\",\"coords\":\"182,90,213,143\"}]"} {"title":"Mass of the electron","description":"Correct!","type":"correct","color":"#000000","code":"[{\"shape\":\"rect\",\"coords\":\"114,104,163,140\"}]"}

Review

Notice that both \(n\) and \(Z\) in Equation 26-21 are dimensionless. Because \(r_n\) is a distance, all of the other terms on the right-hand side, taken as they appear in the equation, must have dimensions of distance as well. This distance, usually written as \(a_0\) and called the Bohr radius, is