Estimate the ground state energy for the Helium atom using both
the time-independent perturbation theory and the WKB approximation
method. Compare the results to make sure they are the same.
Calculate the ground state energy of a helium atom in a box of
1cm on a side.
Solution: these are constants that we will see again and
again. I set c = 1.
In the ground state = 3, the helium mass is about 4 times the
proton mass, and using , the energy is roughly
E = [4(10^6)10(3)]/[2(4)(10^9)(10^16)] ~ 1.5 x 10^(-18)
ev.
This is a small energy, especially when compared to room
temperature energy of .025 ev. You...
Atomic Energy Levels. An atom in the second excited state (n =
3) of H is just barely ionized when a photon strikes the atom—what
is the wavelength of this photon? (Assume that all of the photon’s
energy went into the atom.)
A hydrogen atom is in its second excited state, n =
3.
PART A
Using the Bohr model of hydrogen, find the linear momentum.
PART B
Using the Bohr model of hydrogen, find the angular momentum of
the electron in this atom.
What is the difference between the ground state of an atom and
an excited state of an atom?
Drag the terms on the left to the appropriate blanks on the
right to complete the sentences.
The ground state
The excited state
1. ___________ is when an electron occupies an
unstable higher energy orbital.
2. __________ is the lowest energy state of an
atom in which all electrons are in the lowest possible energy
orbital.
A hydrogen atom is in its second excited state, n =
3.
Using the Bohr model of hydrogen, find the linear momentum.
Using the Bohr model of hydrogen, find the angular momentum of
the electron in this atom.
An electron in a hydrogen atom is excited from the n = 1 ground state to the n = 4 excited state. Classify the statements about this absorption and emission process as true or false. True On average, the electron is closer to the nucleus in the n = 4 state than in the n = 1 state. The wavelength of light absorbed when the electron is excited from the ground state to n = 4 is the same as the wavelength of...
A helium ion with a single electron (denoted He+) is
in an excited state with radius the same as that of the ground
state of hydrogen.
(a) What is n for the He1+ ion?
(b) How much energy in eV is needed to ionize the ion from this
excited state?
eV
A hydrogen atom
(Z = 1)
is in the fourth excited state, and a photon is either emitted
or absorbed.
Concepts:
(i) What is the quantum number of the fourth excited state?
12 345
(ii) When an atom emits a photon, is the final quantum number
nf
of the atom greater than or less than the initial quantum
number ni?
greater thanless than
(iii) When an atom absorbs a photon, is the final quantum
number
nf
of the atom greater than...
Show that the deuteron has no bound excited states by estimating
the excited state energy and comparing it to the potential well.
Consider two cases for the excited state:
a) higher order radial eigenfunctions,
b) non-zero angular momentum.
c) If the nuclear force had a longer range R >R0 we could
possibly have excited states. What would be the minimum and maximum
values of R∗ so that there could be an excited state with l = 1 but
no excited...