In 1885, Johann Balmer, a numerologist, derived the following relation for the wavelength of lines in the visible
spectrum of hydrogen:
Wavelength = 364.6 n²/(n^2 - 4)
where wavelength is in nanometers and n is an integer that can be
3, 4, 5, Show that this relation follows from the Bohr
equation and Equation 5.2. Note that, for the Balmer series, the electron is returning to the n = 2 level.

5.6⋅10−^19  j

do you need the explaination?

a). in this case, dh> 0 and sd> 0. if t becomes larger, the term "-tds" will become more negative. at some point, it is possible that -dts will be more negative than the dh is positive, and the reaction will become spontaneous. this is probably the correct answer, but you should look at all of the other possibilities and make sure of that.

alchemy hadn't scientific methods of study, appeal to mysticism and fantasy, the knowledge of chemistry and physics were modest at that time.

alchemy was - but as new rules were discovered it either changed into chemistry or it became "unscientific".