Which missing item would complete this alpha decay reaction?

257/100 fm= +4/2he

The technique here is to balance the number of particles which is the numerator and the number of protons which is the denominator

Therefore

NUMERATOR:

257 – 4 = 253

DENOMINATOR:

100 – 2 = 98

 the number of protons of an ion is simply its atomic number therefore, from the periodic table

98 = Californium

The answer here is that we will add an Isotope of californium, 253/98 Cf

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".