Answer
Strontium-90 (atomic number 38) should become yttrium-90 (atomic number 39) after beta emission.
Work Step by Step
The atomic number increases by 1 for beta emission, because beta particles carry a charge of -1e. A neutron in the nucleus effectively becomes a proton.
This is discussed on pages 628-629. The periodic table on page 216 is also helpful.
The physicist can test the strontium sample for any yttrium, perhaps by using chemical tests, a mass spectrometer, or other means. To verify that the strontium is a pure beta emitter, she will have to rule out alpha or gamma emission. The radiation detectors described on pages 626-627 will help in that regard. Bubble chambers can distinguish between positively-charged alpha particles and negatively-charged betas, and a scintillation counter is sensitive to gamma radiation.