Question

5. An electron is in an n = 4 state of the hydrogen atom. A) What is its energy? B) What properties besides energy are quantized and what values might be found if these properties were measured? 6. Consider the 3d state. A) Verify that the normalization constant for the 3d radial wave function given in Table 7.4 is correct. B) Verify that one of the associated angular states is properly normalized. (If you have to look up an integral, please give the source of the integral.) C) In this state, where is it most likely to find the electron?

          5. An electron is in an n = 4 state of the hydrogen atom.
A) What is its energy?
B) What properties besides energy are quantized and what values might be
found if these properties were measured?
6. Consider the 3d state.
A) Verify that the normalization constant for the 3d radial wave function given in
Table 7.4 is correct.
B) Verify that one of the associated angular states is properly normalized. (If you
have to look up an integral, please give the source of the integral.)
C) In this state, where is it most likely to find the electron?

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5. An electron is in an n = 4 state of the hydrogen atom.
A) What is its energy?
B) What properties besides energy are quantized and what values might be
found if these properties were measured?
6. Consider the 3d state.
A) Verify that the normalization constant for the 3d radial wave function given in
Table 7.4 is correct.
B) Verify that one of the associated angular states is properly normalized. (If you
have to look up an integral, please give the source of the integral.)
C) In this state, where is it most likely to find the electron?

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University Physics with Modern Physics

Hugh D. Young 14th Edition

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Solved by Expert David Collins

10/19/2022

Step 1

The energy of an electron in the hydrogen atom can be calculated using the formula: E = -13.6 eV / n^2 where E is the energy in electron volts (eV) and n is the principal quantum number. For n = 4, the energy can be calculated as: E = -13.6 eV / (4^2) E = Show more…

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5. An electron is in an n = 4 state of the hydrogen atom. A) What is its energy? B) What properties besides energy are quantized and what values might be found if these properties were measured? 6. Consider the 3d state. A) Verify that the normalization constant for the 3d radial wave function given in Table 7.4 is correct. B) Verify that one of the associated angular states is properly normalized. (If you have to look up an integral, please give the source of the integral.) C) In this state, where is it most likely to find the electron?

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Transcript

00:01 The energy of an electron in a hydrogen atom can be calculated using the equation.

00:08 Energy is equal to negative 2 .178 times 10 to negative 18 joules multiplied by 1 over the energy level squared.

00:21 The energy level is 1.

00:24 Then we get negative 2 .178 times 10 to the negative 18 joules.

00:33 However, if the energy level is infinity, 1 over infinity squared is 0, so that gives us 0 joules.

00:47 So the energy required to eject an electron is the difference in energy between these two.

00:55 It'll be the final state minus the initial state, giving us an energy that is equal to positive 2 .178 times 10 ,000.

01:06 The negative 18 joules.

01:09 0 minus this negative gives us a positive number.

01:17 So this was problem number one.

01:21 Problem number two, how many possible values of l and ml are there when we have n equal to 3? well, if n equals 3, then l can be 0, 1, or 2.

01:46 All the way up to n minus 1.

01:50 When l is 0, ml can only be 0.

01:58 When it is negative 1, sorry, when l is 1, ml can be negative 1, 0, or 1.

02:08 And when l is 2, then ml can be negative 2, negative 1, 0, 1 .1.

02:22 And 2.

02:24 But when we go to n equals 5, then l, we're going to have a few more here...

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