Problem 38
How does de Broglie's hypothesis account for the fact that the energies of the electron in a hydrogen atom are quantized?
Problem 40
Does a baseball in flight possess wave properties? If so, why can we not determine its wave properties?
Problem 41
Thermal neutrons are neutrons that move at speeds comparable to those of air molecules at room temperature. These neutrons are most effective in initiating a nuclear chain reaction among \({ }^{235} \mathrm{U}\) isotopes. Calculate the wavelength (in \(\mathrm{nm}\) ) associated with a beam of neutrons moving at \(7.00 \times 10^{2} \mathrm{~m} / \mathrm{s}\) (mass of a neutron \(=1.675 \times 10^{-27} \mathrm{~kg}\) ).
Problem 42
Protons can be accelerated to speeds near that of light in particle accelerators. Estimate the wavelength (in \(\mathrm{nm})\) of such a proton moving at \(2.90 \times 10^{8} \mathrm{~m} / \mathrm{s}\) (mass of a proton \(\left.=1.673 \times 10^{-27} \mathrm{~kg}\right)\)
Problem 43
What is the de Broglie wavelength (in \(\mathrm{cm}\) ) of a 12.4-g hummingbird flying at \(1.20 \times 10^{2} \mathrm{mph}\) \((1\) mile \(=1.61 \mathrm{~km}) ?\)
Problem 44
What is the de Broglie wavelength (in \(\mathrm{nm}\) ) associated with a 2.5 -g Ping-Pong ball traveling at \(15 \mathrm{mph}\) ?
Problem 45
What are the inadequacies of Bohr's theory?
Problem 46
What is the Heisenberg uncertainty principle? What is the Schrödinger equation?
Problem 47
What is the physical significance of the wave function?
Problem 48
How is the concept of electron density used to describe the position of an electron in the quantum mechanical treatment of an atom?
