Question

A) Sketch a separate diagram for the energy levels of the
electron in the Hydrogen atom – The diagram should be to scale.
Annotate the diagram with the ground state energy E0, the principal
quantum number n, and the ionization energy of the atom (13.6
eV).

B) It is known that a certain hydrogen atom has n=5 and m=2. How
many different states are consistent with this information?

C) Answer the same question (in terms of n and m) for arbitrary
values of n and m.

D) There are many ways of expressing the classical limit of quantum
mechanics. State one of them

Answer #1

A. Consider a hydrogen atom with one electron and quantized
energy levels. The lowest energy level (n = 1) is the ground state,
with energy -13.6 eV. There are four states corresponding to the
next lowest energy (n = 2), each with energy-3.4 eV. For the
questions below, consider one of these four states, called one of
the first excited states.
2. Assume that this hydrogen atom is present in a gas at room
temperature (T ~ 300 K, kBT...

Consider the Bohr model of the hydrogen atom for which an
electron in the ground state executes uniform circular motion about
a stationary proton at radius a0. (a) Find an expression
for the kinetic energy of the electron in the ground state. (b)
Find an expression for the potential energy of the electron in the
ground state. (c) Find an expression for the ionization energy of
an electron from the ground state of the hydrogen atom. The
ionization energy is...

The ionization energy for a hydrogen atom in its ground state is
13.6 eV. Hence the ionization energy for a ground-state He+ ion
is?
Please explain!

5a) Positronium is a bound state of an electron and a positron.
What is the energy of the photon emitted in transitions of
positronium from the first excited state to the ground state? (A)
1.7 eV , (B) 5.1 eV , (C) 6.8 eV , (D) 13.6 eV, (E) 20.4 eV
5b) A new hydrogen-like atom is discovered where the particle
orbiting the proton has mass 2me and charge 2e, where me and e are
the mass and charge 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...

Take the potential energy of a hydrogen atom to be zero for
infinite separation of the electron and proton. Then the ground
state energy of a hydrogen atom is –13.6 eV. The energy of the
first excited state is:
A) 0eV
B) –3.4 eV
C) –6.8 eV
D) –10.2 eV
E) –27 eV

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.)

Quantum Mechanics II (Griffiths)
The hydrogen atom is in state n = 3. What is the energy of the
state in eV? What is the degeneracy? List all possible quantum
numbers l and m.

Consider the first three energy levels of hydrogen (n = 1, 2,
3).
a) What photon energies can be observed from transitions between
these levels? Label these in increasing order as E1,
E2, and E3.
b) A hydrogen atom which is initially in the n = 2 level
collides with an aluminum atom in its ground state (the kinetic
energy of the collision is nearly zero). The hydrogen can drop to
the n = 1 level and ionize the aluminum...

Point out every mistake with the following set of quantum
numbers for an electron in a hydrogen atom, and then write a new,
valid set of quantum numbers with the magnetic value, and find the
energy of that electron for the new quantum numbers you picked
using -13.6 eV for the hydrogen ground-state energy:
(0,1,-2,-3)

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