Question

I have solved some of the questions and the answers are the following

1. 1.62 * 10^-4 eV

2. 0.00765432 m

4. 5.909 * 10^-3 m

5. 3.33 * 10^-10 m

So the only questions missing are question #3 and question #6. If when solving questions 1, 2, 4 and 5, you do not get the same values as posted here, please do not even bother to submit question 3 and question 6 because you most likely have it wrong and I will give you the worst review of your life :)

1.  Suppose that an electron is trapped in a one-dimensional, infinite potential well of width 250 nm is excited from the 2nd excited state to the fifth excited state.

What energy must be transferred to the electron in order to make this transition?

2. What wavelength photon does this correspond to?

3. Considering all of the possible ways that the excited electron can de-excite back down to the ground state, what is the longest wavelength photon that could be emitted?

4. Considering all of the possible ways the electron could de-excite back down to the ground state, what is the shortest wavelength photon that could be emitted?

5. What is the wavelength of an electron in the ground state of a hydrogen atom?

6.  A beam of electrons is incident upon a gas of hydrogen atoms.

What minimum speed must the electrons have to cause the emission of 486 nm light corresponding to the 4 to 2 transitions of hydrogen? Report your answer to 3 significant figures.

Answer 1

3. The energy levels of 1D potential well are

From n=6(fifth excited state) possible deexcitations are:

a. n=5 to n=1

b. n=5 to n=2

c. n=5 to n=3

d. n=5 to n=4

e. n=4 to n=3

f. n=4 to n=2

g. n=4 to n=1

h. n=3 to n=2

i. n=3 to n=1

j. n=2 to n=1

k. n=6 to n=5

l. n=6 to n=4

m. n=6 to n=3

n. n=6 to n=2

o. n=6 to n=1

Now as energy change =

Hence, wavelength will be longest when energy change is minimum

And energy change is directly porportional to

which is minimum for transition j.

Energy change

So  

6.