Question

Let's use the Bohr model equations to explore some properties of the hydrogen atom. We will determine the kinetic, potential, and total energies of the hydrogen atom in the n=2 state, and find the wavelength of the photon emitted in the transition n=2?n=1.

Find the wavelength for the transition *n*=3 ?
*n*=2 for singly ionized helium, which has one electron and
a nuclear charge of 2*e*. (Note that the value of the
Rydberg constant is four times as great as for hydrogen because it
is proportional to the square of the product of the nuclear charge
and the electron charge.)

Express your answer in nanometers to three significant figures.

Answer #1

Kinetic energy = 13.6 / n^{2}

Potential energy = - 2*13.6 / n^{2}

Total energy = - 13.6 / n^{2}

Now, put n = 2 in the above three equations,

we get, Kinetic energy = 3.4 eV , Potential energy = -6.8 eV, Total energy = - 3.4 eV

Energy of emiited photon = -3.4 - (-13.6) = 10.2 eV

Wavelength = hc/Energy

Wavelength = 6.63e-34*3e8 / 10.2*1.6e-19

Wavelength = 1.218e-7 m or 121.8 nm

Another method to solve for wavelength is to use rydberg's constant

1/wavelength = - 1.097e7 (1/2^{2} - 1/1^{2} )
Here 1.097e7 is rydberg's constant

wavelength = 121.8 nm

For Helium ,

1/wavelength = 4.39e7 (1/9 -1 /4)

wavelength = 1.64e-7 m or 164 nm

Singly ionized helium (He+) atom/ion has a single remaining
electron and a nuclear charge of +2? (twice that of a proton).
Using the Bohr model with appropriate modifications, estimate a)
the radius and b) the total energy (in electron volts) of such an
atom in its first excited level. c) When the state of this atom
changes from the first excited level to the ground level, a photon
is emitted in the process. Estimate the energy (in electron volts)
of...

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...

The ionized helium atom can be treated with a Bohr model with
nuclear charge Z=2. The resulting energy levels are four times
those of the hydrogen atom:
Ehelium=4Ehydrogen= -(54.4eV)/n^2
From those energy levels, calculate the wavelengths of spectral
lines from ionized helium for transitions that end on nf=1. Do any
of these lie in the visible range? Would any spectral lines of
ionized helium lie in the visible range?

why are the electrons of the helium atom not all in the 1s
state.
Which of the following
choices best explains this observation?
Coulomb's law
the Pauli exclusion principle
the Einstein quantum entanglement principle
Rutherford's explanation of atomic structure
the Heisenberg uncertainty principle
2.)There is a singly-ionized helium atom, which has 2 protons
with its remaining electron in the ground state.
Using the Bohr model calculation, determine the maximum
wavelength in nanometers for a photon that could remove the
remaining...

For a hydrogen atom, calculate the wavelength of an emitted
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explains the line spectrum of hydrogen. What is the
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electrons dropped from the n=6 state to the n=2 state. In what
region of the electromagnetic spectrum does this wavelength fall?
Which color line is this in the line spectra of hydrogen?

a. what is the energy of the emitted photon if an electron in
the hydrogen atom makes a transition from the n=7 state to the n=2
state?
b. Now, Imagine there is a photon with the same wavelength. What
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An electron in a hydrogen atom makes a transition from the n = 7
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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
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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
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c. When the electron returns from its excited...

Problem 1.18
Values for some properties of the n = 1 state of the Bohr
model of the hydrogen atom are given in the following table. Write
the value of the same parameter (in the same units) for the
n = 2 state.
parameter
n = 1
n = 2
momentum (kgms)
1.99 ⋅ 10-24
de Broglie wavelength (nm)
0.333
kinetic energy (Eh)
0.500
transition energy to n = 3 (Eh)
0.444
Part A
Determine the momentum for the n...

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