Question

This problem deals with the probabilistic interpretation of the hydrogen wavefunction.

a. Calculate the probability that a hydrogen 1s electron will be
found within a distance of 2a_{0} from the nucleus.

b. Calculate the radius of the sphere that encloses a 50% probability of finding a hydrogen 1s electron.

c. Calculate the radius of the sphere that encloses a 90% probability of finding a hydrogen 1s electron.

Answer #1

It may assist you to solve your problem.

Consider the Schrodinger equation and its solution for the
hydrogen atom.
a) Write an equation that would allow you to calculate, from the
wavefunction, the radius of a sphere around the hydrogen nucleus
within which there is a 90% probability of finding the electron.
What is the radius of the same sphere if I want a 100% probability
of finding the electron?
b) Calculate the shortest wavelength (in nm) for an electronic
transition. In what region of the spectrum is...

(a) If the radial part of a particle’s wavefunction is R(r),
what is the probability of finding the particle somewhere between
radius r1 and r2?
(b) Write down the radial wavefunction R10(r) for the n
= 1, l = 0 state of the hydrogen atom. The nucleus of the hydrogen
atom is a proton, which has a radius rp =
1015 m. Write down an approximate expression for
R10(r) which is valid for r ≤ rp. What is the
probability...

Based on the solutions to the Schrödinger equation for the
ground state of the hydrogen atom, what is the probability of
finding the electron within (inside) a radial distance of
3.5a0 (3.5 times the Bohr radius) of the nucleus?
Express the probability as a decimal (for example, 50% would be
expressed as 0.50).

Using the radial probability density, calculate (a) the average
distance between the nucleus and the 2s electron of the hydrogen
atom and (b) the average distance between the nucleus and the 2p
electron of the hydrogen atom. (c) Compare these results with the
radius value(s) predicted by Bohr’s atomic model for these
electrons. Note: Clearly show all your math steps leading to the
final answer

The ”most-probable” distance from the nucleus to observe the
electron in a 1H hydrogen atom in its ground state is the Bohr
radius, a0= 5.29×10^−11m. What is the probability of
observing the electron in a ground state hydrogen atom somewhere
within any greater distance r from the nucleus a0 ≤ r
<∞?

3. [10 pts] Calculate the radius of the sphere that encloses 92%
of the ground state of the hydrogen atom. Express your answer in
Ångstroms and you must explicitly integrate over r, ϕ and θ.
HINT: This problem cannot be solved analytically, and there will
be a point where the solution must be found numerically. Tabulate
your trial and error numerical solution. You can use a spreadsheet
program like Excel to solve for the radii within one decimal place
by...

in the problem, you can assume a "hydrogen-like" nucleus. You
have a selenium atom, with an electron in the 5th excited state.
The electron undergoes spontaneous emission and Is in the third
excited state.
a.) what is the energy of the photon emitted?
b.) what is the frequency of the photon?
c.) what is the difference in the radius of the orbits?

A hydrogen atom is made up of a proton of
charge +Q = 1.60 x10-19 C and an
electron of charge –Q= –1.60 x
10-19 C. The proton may be regarded as a point charge at
the center of the atom. The motion of the electron causes its
charge to be "smeared out" into a spherical distribution around the
proton, so that the electron is equivalent to a charge per unit
volume of ρ ( r ) = − Q...

Physical Chemistry Problem:
The ‘size’ of an atom is sometimes considered to be measured by
the radius of a sphere that contains 90% of the charge density of
the electrons in the outermost occupied orbital. Calculate the
‘size’ of a hydrogen atom in its ground state according to this
definition. (b) Consider how the ‘size’ of a hydrogen atom would
change if an alternate definition of size were used. Generate a
plot of P vs r that shows how this...

Energy, Wavelength, Frequency Problem: Show your work neatly and
methodically.
Consider an electron in the hydrogen atom giving off light which
has a wavelength of 625 nm, according to the Balmer Series.
a) From what energy level in the hydrogen atom did the electron
fall to emit this light?
b) What is the frequency of this light?
c) What is the energy of this light?
2. a) Use the de Broglie relationship to determine the
wavelength of a 85 kg...

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