Watch the spelling. It's "Ptolemy", not "Ptolomy". 
I'm no expert on identifying the particular Ptolemy responsible for issuing particular coins, but This link illustrates all the known types of Ptolemaic bronzes that are about 36mm diameter. From this, I'd say you are correct; it's a coin of Ptolemy II. "Hemidrachm" is just one opinion on what this denomination might be called; we simply don't know for sure. Collectors call them an AE36 - meaning "bronze, 36mm".
I'm no expert on identifying the particular Ptolemy responsible for issuing particular coins, but This link illustrates all the known types of Ptolemaic bronzes that are about 36mm diameter. From this, I'd say you are correct; it's a coin of Ptolemy II. "Hemidrachm" is just one opinion on what this denomination might be called; we simply don't know for sure. Collectors call them an AE36 - meaning "bronze, 36mm".
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis























