1 You have an electron in a two dimensional quantum box that is 8 43 nm wide and 8 43 nm Calculate the energies of the lowest 3 states, and write down their wavefunctions 2 The Bohr radius is given by 0 h2 e2 me Look up the constants and calculate the value of this expression Starting from the units of the constants you used, show that your Bohr radius has units of meters 3 Show that the g( ) we guessed in Lecture 32 is indeed a solution to the part of the Schroedinger equation for the hydrogen atom 4 Calculate the mean value of r for an electron in the ground state of a hydrogen atom The mean value is given by 14100 dV 14 100 4mr dr

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Question: 1. You have an electron in a two-dimensional quantum box that is 8.43 nm wide and 8.43 nm. Calculate the energies of the lowest 3

1. You have an electron in a two-dimensional quantum box that is 8.43 nm wide and 8.43 nm. Calculate the energies of the lowest 3 states, and write down their wavefunctions.

2. The Bohr radius is given by ?0 h2 / [? e2 me]. Look up the constants and calculate the value of this expression.

Starting from the units of the constants you used, show that your Bohr radius has units of meters.

3. Show that the g(?) we guessed in Lecture #32 is indeed a solution to the ? part of the Schroedinger equation for the hydrogen atom.

4. Calculate the mean value of r for an electron in the ground state of a hydrogen atom. The mean value is given by

1. You have an electron in a two-dimensional quantum box that is

"14100/ dV - 14/100/4mr dr

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