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.

A large number of ground state electrons in a gas of hydrogen
atoms are excited to the fourth excited state.
a. How many energy did each electron gain?
b. How many visible photos would be emitted by these electrons
as they return to the ground state?
c. What is the wavelength (in nm) of the least energetic visible
photon?

Answer the following questions using the Bohr model of the
hydrogen atom.
a) A hydrogen atom is the n = 3 excited state when its electron
absorbs a photon of energy 4.40 eV. Draw a diagram roughly to
scale, of relevant energy levels for this situation. Make sure to
show and label the initial energy of the H atom in the n=3 state,
the energy level at which this atom loses its electron, and kinetic
energy of the electron.
b)What...

1. a. A photon is absorbed by a hydrogen atom causing an
electron to become excited (nf = 6) from the ground state electron
configuration. What is the energy change of the electron associated
with this transition?
b. After some time in the excited state, the electron falls from
the n = 6 state back to its ground state. What is the change in
energy of the electron associated with this transition?
c. When the electron returns from its excited...

The hydrogen atomic emission spectrum includes a UV line with a
wavelength of 92.323 nm. Photons of this wavelength are emitted
when the electron transitions to nf = 1 as the final
energy state. Show all steps and round answers to correct sig
figs.
a) Is this line associated with a transition between different
excited states or between an excited state and the ground
state?
b) What is the energy of the emitted photon with wavelength
92.323 nm?
c) What...

A hydrogen atom transitions from the n = 6 excited state to the
n = 3 excited state, emitting a photon.
a) What is the energy, in electron volts, of the electron in the
n = 6 state? How far from the nucleus is the electron?
b) What is the energy, in electron volts, of the photon emitted
by the hydrogen atom? What is the wavelength of this photon?
c) How many different possible photons could the n = 6...

4 a) A hydrogen atom in the ground state absorbs a photon of
wavelength 97.2 nm. What energy level does the electron reach?
b) This excited atom then emits a photon of wavelength 1875.4
nm. What energy level does the electron fall to?

1. A hydrogen atom, initially in the first excited state
(initial ni = 2), absorbs a photon of wavelength 656.30 nm.
(a) (5) What is the final state ? In other words, solve for the
FINAL nf . Show all work.
(b) (5) What would be the wavelength of a photon, which , when
absorbed by the atom, ionizes an electron from the first excited
level ?
2. X-rays with initial wavelength λ = 0.0665 nm undergo Compton
scattering.
(a)...

An electron in an excited state
of a hydrogen atom emits two photons in succession, the first at
3037 nm and the second at 94.92 nm, to return to the ground state
(n=1). For a given transition, the wavelength of the emitted photon
corresponds to the difference in energy between the two energy
levels.
What were the principal quantum numbers of the initial and
intermediate excited states involved?

Suppose that an electron trapped in a one-dimensional infinite
well of width 0.341 nm is excited from its first excited state to
the state with n = 5.
1 What energy must be transferred to the electron for this
quantum jump?
2 The electron then de-excites back to its ground state by
emitting light. In the various possible ways it can do this, what
is the shortest wavelengths that can be emitted?
3 What is the second shortest?
4 What...

A hydrogen atom in the ground state absorbs a photon of
wavelength 95.0 nm.
What energy level does the electron reach?
This excited atom then emits a photon of wavelength 434.1 nm.
What energy level does the electron fall to?
-I know this question has already been asked on Chegg but each
question I go to has different calculations and I can't get the
right answer.

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