# Serial of year 36

## Text of serial

## Tasks

### (10 points)1. Series 36. Year - S. search for quanta

Find the Rydberg constant's value and determine which hydrogen spectral lines belong to the visible spectrum. These lines are the only ones Rydberg could use to discover his formula, as neither UV nor IR spectra could yet be measured. What color are they, and which transitions in the Bohr model do they correspond to? (3pts)

Calculate de Broglie wavelength of your body. How does this value compare to the size of an atom or atomic nucleus? (3pts)

Assume you have a cuvette with $10 \mathrm{ml}$ of fluorescein water solution. Then, you point an argon laser at the cuvette. The laser is characterized by a wavelength of $488 \mathrm{nm}$ and a power of $10 \mathrm{W}$. At the same time, the fluorescein molecule fluoresces at a wavelength of $521 \mathrm{nm}$ with a quantum yield (proportion of absorbed photons that are emitted back) of $95 \mathrm{\%}$. If the initial temperature of the cuvette is $20 \mathrm{\C }$, how long will it take for its contents to start boiling? Assume that the cuvette is perfectly thermally insulated, the laser beam is fully absorbed in it, and the amount of fluorescein is negligible in terms of heat capacity. (4pts)