You say "this diagram" and then provide a link to a whole page with several diagrams
and no clear component values...
You want about 1k to 2k base resistor, emitter to ground, collector to IR LED + current limit
resistor (about 100 ohms, other end to 5V supply - you'll get about 40mA then
The '2222 will switch in < 0.3us worst case with 15mA load, probably < 1us for
40mA, so no issue with switching speed.