"Estimate the power radiation by a ____ cm object at ______ K (temperature)"
"What is the peak wavelength emitted by the blackbody/object at a certain temperature"
"The position and momentum of a particle cannot be simultaneously measured with arbitrarily high precision. There is a minimum for the product of the uncertainties of these two measurements. There is likewise a minimum for the product of the uncertainties of the energy and time."
Some important things to take away from this lecture:
The electronic mass is replaced by the reduced mass -- this is a useful trick for decomposing a two-body system with masses m1 and m2 that revolve about each other (such as the hydrogen atom, nucleus plus orbiting electron)....into a one body of reduced mass u revolving about the other mass that then has a fixed position (ie it is infinitely massive). **In other words, we simplify a two body problem into a one body problem! :)
Bohr's revised model is very successful for hydrogenic atoms but seriously flawed in other ways: "It cannot be extended to atoms or ions with more than one electron.
- It cannot offer any explanation for the different intensities of the various transitions.
- It does not explain why many lines are found, at high resolution, to actually be composed of closely associated groups of lines. (Such groups are known as multiplets.)
- Most damagingly, there is no justification for the assumptions made as the basis of the derivation. For example, there is no obvious reason for the angular momenta to be quantised into units of h/2π , this appears to form part of the theory solely as a convenience to make the theory work!"
For questions asking about the "series limit" of the Balmer or Lyman series, this is simply calculating the limit of the series as n2 goes to infinity. In this case, the n1^2 term predominates and becomes the only term in the parentheses. You simply multiply 1/n1^2 times the Rydberg constant to get the wavelength limit of the series in question (in the case of the Balmer series, n1 is set to 2...so after you square it you simply get 109680 * (1/4) cm-1 = 2.742 x 10^4 cm-1....or about 364.7 nm). The Lyman series limit is wavelength 91.2 nm.