Problem 64
Calculate the wavelength of light emitted when each of the following transitions occur in the hydrogen atom. What type of electromagnetic radiation is emitted in each transition? a. \(n=4 \rightarrow n=3\) b. \(n=5 \rightarrow n=4\) c. \(n=5 \rightarrow n=3\)
Problem 67
Consider only the transitions involving the first four energy levels for a hydrogen atom: a. How many emissions are possible for an electron in the \(n=4\) level as it goes to the ground state? b. Which electronic transition is the lowest energy? c. Which electronic transition corresponds to the shortest wavelength emission?
Problem 68
Assume that a hydrogen atom's electron has been excited to the \(n=5\) level. How many different wavelengths of light can be emitted as this excited atom loses energy?
Problem 69
Does a photon of visible light \((\lambda \approx 400 \text { to } 700 \mathrm{nm})\) have sufficient energy to excite an electron in a hydrogen atom from the \(n=1\) to the \(n=5\) energy state? from the \(n=2\) to the \(n=6\) energy state?
Problem 70
An electron is excited from the \(n=1\) ground state to the \(n=\) 3 state in a hydrogen atom. Which of the following statements are true? Correct the false statements to make them true. a. It takes more energy to ionize (completely remove) the electron from \(n=3\) than from the ground state. b. The electron is farther from the nucleus on average in the \(n=3\) state than in the \(n=1\) state. c. The wavelength of light emitted if the electron drops from \(n=3\) to \(n=2\) will be shorter than the wavelength of light emitted if the electron falls from \(n=3\) to \(n=1 .\) d. The wavelength of light emitted when the electron returns to the ground state from \(n=3\) will be the same as the wavelength of light absorbed to go from \(n=1\) to \(n=3\) e. For \(n=3,\) the electron is in the first excited state.
Problem 71
Calculate the maximum wavelength of light capable of removing an electron for a hydrogen atom from the energy state characterized by \(n=1,\) by \(n=2\)
Problem 72
Consider an electron for a hydrogen atom in an excited state. The maximum wavelength of electromagnetic radiation that can completely remove (ionize) the electron from the H atom is 1460 \(\mathrm{nm}\) . What is the initial excited state for the electron \((n=?) ?\)
Problem 73
An excited hydrogen atom with an electron in the \(n=5\) state emits light having a frequency of \(6.90 \times 10^{14} \mathrm{s}^{-1} .\) Determine the principal quantum level for the final state in this electronic transition.
Problem 75
Using the Heisenberg uncertainty principle, calculate \(\Delta x\) for each of the following. a. an electron with \(\Delta v=0.100 \mathrm{m} / \mathrm{s}\) b. a baseball (mass \(=145 \mathrm{g} )\) with \(\Delta v=0.100 \mathrm{m} / \mathrm{s}\) c. How does the answer in part a compare with the size of a hydrogen atom? d. How does the answer in part b correspond to the size of a baseball?
Problem 76
The Heisenberg uncertainty principle can be expressed in the form $$\Delta E \cdot \Delta t \geq \frac{h}{4 \pi}$$ where \(E\) represents energy and \(t\) represents time. Show that the units for this form are the same as the units for the form used in this chapter: $$\Delta x \cdot \Delta(m v) \geq \frac{h}{4 \pi}$$
