Give 2 problems with solution about Rayleigh-Jeans Law

The diffraction of radiation can be used to determine the spacing between atoms. In practice, the wavelength of the radiation used should be restricted to a value which is of the same order of magnitude as the interatomic distances to be determined. Such experiments are commonly performed using X-rays (electromagnetic radiation), however a beam of subatomic particles, such as of neutrons or electrons, may also be used if their corresponding de Broglie wavelength is of the appropriate magnitude. Calculate the de Broglie wavelength of a neutron (mn = 1.67493×10-27 kg) moving at one four hundredth of the speed of light (c/400). (Enter at least 4 significant figures.) Calculate the velocity of an electron (me = 9.10939×10-31 kg) having a de Broglie wavelength of 167.1 pm.

Astronomers observe the chromosphere of the Sun with a filter that passes the red hydrogen spectral line of wave- length 656.3 nm, called the H line. The filter consists of a transparent dielectric of thickness d held between two par- tially aluminized glass plates. The filter is kept at a constant temperature. (a) Find the minimum value of d that will pro- duce maximum transmission of perpendicular H, light if the dielectric has an index of refraction of 1.378. (b) If the tem- perature of the filter increases above the normal value increas- ing its thickness, what happens to the transmitted wavelength? (c) The dielectric will also pass what near-visible wavelength? One of the glass plates is colored red to absorb this light.

For a 2000K blackbody, by what percentage is the Rayleigh–Jeans law in error at wavelengths of 1.0 mm?