Problem 49
What is an atomic orbital? How does an atomic orbital differ from an orbit?
Problem 50
Alveoli are tiny sacs of air in the lungs. Their average diameter is \(5.0 \times 10^{-5} \mathrm{~m} .\) Calculate the uncertainty in the velocity of an oxygen molecule \(\left(5.3 \times 10^{-26} \mathrm{~kg}\right)\) trapped within a sac. (Hint: The maximum uncertainty in the position of the molecule is given by the diameter of the sac.)
Problem 52
In the beginning of the twentieth century, some scientists thought that a nucleus may contain both electrons and protons. Use the Heisenberg uncertainty principle to show that an electron cannot be confined within a nucleus. Repeat the calculation for a proton. Comment on your results. Assume the radius of a nucleus to be \(1.0 \times 10^{-15} \mathrm{~m}\). The masses of an electron and a proton are \(9.109 \times 10^{-31} \mathrm{~kg}\) and \(1.673 \times 10^{-27} \mathrm{~kg},\) respectively. (Hint: Treat the radius of the nucleus as the uncertaintv in position.)
Problem 53
Suppose that photons of blue light \((430 \mathrm{nm})\) are used to locate the position of a 2.80 -g Ping-Pong ball in flight and that the uncertainty in the position is equal to one wavelength. What is the minimum uncertainty in the speed of the Ping-Pong ball? Comment on the magnitude of your result.
Problem 54
Describe the four quantum numbers used to characterize an electron in an atom.
Problem 55
Which quantum number defines a shell? Which quantum numbers define a subshell?
Problem 56
Which of the four quantum numbers \(\left(n, \ell, m_{\ell}, m_{s}\right)\) determine (a) the energy of an electron in a hydrogen atom and in a many- electron atom, (b) the size of an orbital, (c) the shape of an orbital, (d) the orientation of an orbital in space?
Problem 57
An electron in a certain atom is in the \(n=2\) quantum level. List the possible values of \(\ell\) and \(m_{\ell}\) that it can have.
Problem 58
An electron in an atom is in the \(n=3\) quantum level. List the possible values of \(\ell\) and \(m_{\ell}\) that it can have.
Problem 59
List all the possible subshells and orbitals associated with the principal quantum number \(n\), if \(n=4\).
