- Please Solve All The Sub Questions 1 (120.39 KiB) Viewed 434 times
Please solve all the sub questions :)
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answerhappygod
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Please solve all the sub questions :)
Please solve all the sub questions
5. The wave functions for the hydrogen atom can be written in terms of the three-dimensional spherical coordinates (r, 0, 0) as Pn.l.m₂ (r,0,0) = R₁,t(r)Y₁¸m² (0,0). (3) (a) Identify the variables corresponding to the quantum numbers n, I and my and write down the range of values for each one. What other quantum number is needed to complete the description of the state of the electron? (b) Normalise the following wave function for an electron in the 1s state 1,0,0 (1, 0, 0) xx exp (-1). (4) Hint: You may find the following identity useful [ªr" exp(-ax) dx = n! a¯(2+1), (c) Using the normalised wave function found in (b), calculate the expectation value (1/²) for the 1s state. (d) The 1s wave function from (b) has its maximum value at r = 0, while the radial probability density for the 1s state peaks at r = a, and is zero at r = 0. Explain this apparent paradox.
5. The wave functions for the hydrogen atom can be written in terms of the three-dimensional spherical coordinates (r, 0, 0) as Pn.l.m₂ (r,0,0) = R₁,t(r)Y₁¸m² (0,0). (3) (a) Identify the variables corresponding to the quantum numbers n, I and my and write down the range of values for each one. What other quantum number is needed to complete the description of the state of the electron? (b) Normalise the following wave function for an electron in the 1s state 1,0,0 (1, 0, 0) xx exp (-1). (4) Hint: You may find the following identity useful [ªr" exp(-ax) dx = n! a¯(2+1), (c) Using the normalised wave function found in (b), calculate the expectation value (1/²) for the 1s state. (d) The 1s wave function from (b) has its maximum value at r = 0, while the radial probability density for the 1s state peaks at r = a, and is zero at r = 0. Explain this apparent paradox.