Question

1) A quantum harmonic oscillator with frequency
*ω*contains 41 electrons. What is the energy of the
highest-energy electron? Assume that the electrons are in the
lowest states possible.

2 a) An atom has a total of 18 electrons. What is the principal quantum number of the outermost shell?

2 b) How many electrons does the outermost shell shell contain?

3) Which of the following represents the possible range of integer values for the magnetic quantum number?

a) 1 to l

b) -n to +n

c) 0 to n

d) 0 to l

e) 1 to n

f) -l to +l

4) Suppose the orbital quantum number for an electron in the hydrogen atom is 4. How many orientations of the angular momentum vector are possible?

Answer #1

2 a) Given that an atom has a total of 18 electrons.

Electronic configuration = 1s^{2} 2s^{2}
2p^{6} 3s^{2} 3p^{6}

Hence, principal quantum number of the outermost shell = 3

b) How many electrons does the outermost shell shell
contain = 3s^{2} 3p^{6} = 8

3) possible range of integer values for magnetic quantum number = -l to +l

4) Given that orbital quantum number for an electron in the hydrogen atom is 4.

i.e l = 4

no of orientations of the angular momentum vector = 2l+1 = 2.4 + 1 = 9

The electron in a hydrogen atom with an energy of -0.544 eV is
in a subshell with 18 states.
A. What is the principal quantum number, n, for this atom? n
=
b. What is the maximum possible orbital angular momentum this
atom can have? L=
c. Is the number of states in the subshell with the next lowest
value of ℓℓ equal to 16, 14, or 12?
d. explain part (c.)

A hydrogen atom stays in the 3rd excited state (n = 4). Consider
of the quantum behavior of the electron, but ignore the quantum
behavior of the nucleus. (a) What are the possible values for the
quantum number l and what are the corresponding orbitals? Write
down the magnitude of each orbital angular momentum (in units of
ħ). (b) For each value of l, what are possible values for the
quantum number ml and the magnitude of the z component...

A) What is the energy in joules of an electron in the L-shell of
H-atom?
B) If this electron absorbs a photon with a wavelength of
1.876µm, what is the new energy of the electron and to which shell
will it move?
C) What is the energy of an electron in the M-Shell of a
hydrogen-like quadruple-ionized boron, B++++?
D) In accordance with the quantum mechanical model, list and
tabulate all possible states that the M-shell atom can have and...

An atom has a total of 18 electrons.
a)What is the principal quantum number of the outermost shell?
In detail
b)How many electrons does the outermost shell shell contain? In
detail

A hydrogen atom is in the 6g state.
Determine the principal quantum number.
Determine the energy of the state.
Determine the quantum number ℓ.
Determine the orbital angular momentum.
Determine the possible values for the magnetic quantum
number.

Question 3
Part B:How many values of ml are possible for an
electron with orbital quantum number l = 1?
Express your answer as an integer.
Part C
The quantum state of a particle can be specified by giving a
complete set of quantum numbers (n,l,
ml,ms). How many different
quantum states are possible if the principal quantum number is
n = 2?
To find the total number of allowed states, first write down the
allowed orbital quantum numbers l,...

For the 3d state (orbital) of the hydrogen atom, the principal
quantum number n=3. The orbital quantum number l = 2. For an
electron with these quantum numbers, what is the smallest angle (in
degrees) that an electron's spin axis (angular momentum axis) can
make with respect to an applied magnetic field?

Which of the following states of the hydrogen atom, as defined
only by the principal quantum number, orbital angular momentum
quantum number, and magnetic quantum number, is allowed?
a.
n=0, l =2,ml =1
b.
n=5, l =2,ml =3
c.
n=0, l =2,ml =2
d.
n=5, l =2,ml =0
e.
n=2, l =2,ml =0

A nitric oxide molecule is in a rotational energy level
described by rotational quantum number l=7. The rotational constant
for NO is 1.695 cm-1.
what is the angular momentum?
how many different spatial orientations can this angular
momentum vector take?
what is its rotational energy in Joules?
How much energy (in Joules) is required to excite it to the l=8
level?
What is its rotational frequency?

1- For some atom, consider an electron shell corresponding to a
principal quantum number n. Answer the questions (a)-(b) below. (a)
What is the number of electrons in a fully occupied subshell with a
given orbital quantum number l? Explain your answer. (b) What is
the number of electrons in a fully occupied shell with a given
principal quantum number n? Explain your answer. Hint: For the part
(b), use the known mathematical formulas for finite sums: 1 ? ?=0...

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