The normalized energy eigenfunction of the ground state of the hydrogen atom is given by p(r) = Cexp(-) where a, is the Bohr radius. For this state, calculate: 1.1 The normalization constant C. 1.2 The expectation value of r. 1.3 The expectation value of the potential energy of the electron. 1.4 The standard deviation ofr.
The normalized energy eigenfunction of the ground state of the hydrogen atom is given by p(r) = Cexp(-) where a, is the Bohr radius. For this state, calculate: 1.1 The normalization constant C. 1.2 The expectation value of r. 1.3 The expectation value of the potential energy of the electron. 1.4 The standard deviation ofr.
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Transcribed Image Text:Question 1
The normalized energy eigenfunction of the ground state of the hydrogen atom is given by
Þ(r)
Сехр(- а)
where a, is the Bohr radius. For this state, calculate:
1.1 The normalization constant C.
1.2 The expectation value of r.
1.3 The expectation value of the potential energy of the electron.
1.4 The standard deviation of r.
1.5 The probability that the electron is in a sphere of radius ao.
п!
(Hint: | r"e-ar dr =
an+1»n > -1)
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