Question

I need help solving the problem. For 2) what value do I  use for a? 4) am I to use the tables labeled a) and b)? If so how?

ibnongA
Homework questions:
1. Sketch the first three wavefunctions (w vs x for n = 1, 2 and 3) for the particle in a box.
Alongside these, sketch the first three radial wavefunctions (Rns VS r) for an electron in the 1s, 2s,
and 3s orbitals of hydrogen. How are the two cases similar; and different?
%3D
2. Justify your sketch for the n= 3 particle in a box by making a table of values for y when x = 0,
a, (1/3)a, (2/3)a, (1/4)a, (1/2)a, and (3/4)a, where y = sin(ntx/a), [we are ignoring the normalization
factor for this purpose] and then plotting the points. (You do not need to use graph paper; a sketch
is sufficient, but do show that the calculated points are consistent with it.)
%3D
%3D
%3D
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Transcribed Image Text:ibnongA Homework questions: 1. Sketch the first three wavefunctions (w vs x for n = 1, 2 and 3) for the particle in a box. Alongside these, sketch the first three radial wavefunctions (Rns VS r) for an electron in the 1s, 2s, and 3s orbitals of hydrogen. How are the two cases similar; and different? %3D 2. Justify your sketch for the n= 3 particle in a box by making a table of values for y when x = 0, a, (1/3)a, (2/3)a, (1/4)a, (1/2)a, and (3/4)a, where y = sin(ntx/a), [we are ignoring the normalization factor for this purpose] and then plotting the points. (You do not need to use graph paper; a sketch is sufficient, but do show that the calculated points are consistent with it.) %3D %3D %3D
4. (a) Plot values of E for values of n = 1 to 5, in units of h?/8ma?.
these units.
(L.e., when n= 1,
(b) Plot values of E for values of a = 2* to 6 in units of n?h?/8m.
[*n=1 distorts the scale too much on this graph]
Comments: You should find that energy spacings
increase with n. If you relate this to what you
know about the hydrogen atom, you will see a
large contrast. The difference has to do with the
existence of the electrical potential in the atom.
Energy spacings decrease as the length of
the box increases. You may conclude that by
the time one reached boxes of macroscopic length,
these spacings would exist, but would be much too
small to result in any detectable effects.
(b)
(a)
1111
expand button
Transcribed Image Text:4. (a) Plot values of E for values of n = 1 to 5, in units of h?/8ma?. these units. (L.e., when n= 1, (b) Plot values of E for values of a = 2* to 6 in units of n?h?/8m. [*n=1 distorts the scale too much on this graph] Comments: You should find that energy spacings increase with n. If you relate this to what you know about the hydrogen atom, you will see a large contrast. The difference has to do with the existence of the electrical potential in the atom. Energy spacings decrease as the length of the box increases. You may conclude that by the time one reached boxes of macroscopic length, these spacings would exist, but would be much too small to result in any detectable effects. (b) (a) 1111
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