De Broglie Wavelength Problems
1]
A bacterium (
) in the blood is moving at 0.33 m/s. What is the de
Broglie wavelength of this bacterium?
2]
How fast does a proton have to be moving in order to have the same de Broglie
wavelength as an electron that is moving with a speed of
3]
?
A particle has a de Broglie wavelength of
. Then its kinetic energy doubles.
What is the particle’s new de Broglie wavelength, assuming that relativistic effects can be
ignored?
Line Spectra and the Bohr Model
1]
The electron in a hydrogen atom is in the first excited state, when the electron acquires an
additional 2.86 eV of energy. What is the quantum number n of the state into which the
electron moves?
2]
Using the Bohr model, determine the ratio of the energy of the nth orbit of a triply
ionized beryllium atom (Be3+, Z = 4) to the energy of the nth orbit of a hydrogen atom
(H).
3]
A singly ionized helium atom (He+) has only one electron in orbit about the nucleus.
What is the radius of the ion when it is in the second excited state?
4]
(a) What is the minimum energy (in electron volts) that is required to remove the electron
from the ground state of a singly ionized helium atom (He+, Z = 2)? (b) What is the
ionization energy for He+?
5]
A hydrogen atom is in the ground state. It absorbs energy and makes a transition to the
n = 3 excited state. The atom returns to the ground state by emitting two photons. What
are their wavelengths?
6]
In the hydrogen atom the radius of orbit B is sixteen times greater than the radius of orbit
A. The total energy of the electron in orbit A is −3.40 eV. What is the total energy of the
electron in orbit B?
7]
The energy of the n = 2 Bohr orbit is −30.6 eV for an unidentified ionized atom in which
only one electron moves about the nucleus. What is the radius of the n = 5 orbit for this
species?