Chapter 4: Problem 13
Is it possible to get a continuous emission spectrum from hydrogen?
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These are the key concepts you need to understand to accurately answer the question.
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Chapter 4: Problem 13
Is it possible to get a continuous emission spectrum from hydrogen?
These are the key concepts you need to understand to accurately answer the question.
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What examples of degeneracy in classical physics, other than planetary motion, can you think of?
In a collision between an \(\alpha\) particle and an electron, what general considerations limit the momentum transfer? Does the fact that the force is Coulombic play any role in this respect?
What is the energy, momentum, and wavelength of a photon that is emitted by a hydrogen atom making a direct transition from an excited state with \(n=10\) to the ground state? Find the recoil speed of the hydrogen atom in this process.
(a) Show that in the ground state of the hydrogen atom the speed of the electron can be written as \(v=\alpha c\) where \(\alpha\) is the fine-structure constant. (b) From the value of \(\alpha\) what can you conclude about the neglect of relativistic effects in the Bohr calculations?
Show that the number of \(\alpha\) particles scattered by an angle \(\Theta\) or greater in Rutherford scattering is $$ \left(\frac{1}{4 \pi \epsilon_{0}}\right)^{2} \pi I \rho t\left(\frac{z Z e^{2}}{M v^{2}}\right)^{2} \cot ^{2}(\Theta / 2) $$
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