Chapter 4: Problem 17
Is the ionization energy of deuterium different from that of hydrogen? Explain.
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Chapter 4: Problem 17
Is the ionization energy of deuterium different from that of hydrogen? Explain.
These are the key concepts you need to understand to accurately answer the question.
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Show that the number of \(\alpha\) particles scattered by an angle \(\Theta\) or greater in Rutherford scattering is $$ \left(\frac{1}{4 \pi \epsilon_{0}}\right)^{2} \pi I \rho t\left(\frac{z Z e^{2}}{M v^{2}}\right)^{2} \cot ^{2}(\Theta / 2) $$
(a) Show that when the recoil kinetic energy of the atom, \(p^{2} / 2 M\), is taken into account the frequency of a photon emitted in a transition between two atomic levels of energy difference \(\Delta E\) is reduced by a factor which is approximately \(\left(1-\Delta E / 2 M c^{2}\right)\). (Hint: The recoil momentum is \(p=h v / c .\) ) (b) Compare the wavelength of the light emitted from a hydrogen atom in the \(3 \rightarrow 1\) transition when the recoil is taken into account to the wavelength without accounting for recoil.
In a Franck-Hertz type of experiment atomic hydrogen is bombarded with electrons, and excitation potentials are found at \(10.21 \mathrm{~V}\) and \(12.10 \mathrm{~V}\). (a) Explain the observation that three different lines of spectral emission accompany these excitations. (Hint: Draw an energy-level diagram.) (b) Now assume that the energy differences can be expressed as \(h v\) and find the three allowed values of \(v\). (c) Assume that \(v\) is the frequency of the emitted radiation and determine the wavelengths of the observed spectral lines.
Apply Bohr's model to singly ionized helium, that is, to a helium atom with one electron removed. What relationships exist between this spectrum and the hydrogen spectrum? wavelength of the single photon emitted. into what level was the electron captured?
For the Bohr hydrogen atom orbits, the potential energy is negative and greater in magnitude than the kinetic energy. What does this imply?
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