why the alarm dosn't work when the iphone off?

Because off is off. Unlike dumb phones, the iPhone is basically a computer that can make phone calls. When you put it in standby, processes continue to run. Important processes like maintaining a connection to the cellular network and keeping track of the time. When you shut it off, it's off. Nothing happens when it's off.

"Standby" (or "Sleep" is the phone's normal state when not in use. "Off" is when the phone is totally shut down by holding down the Sleep button the doing the "Slide to Power Off" on the screen.

If you believe it is dangerous to be in the same room as an iPhone, your question is pointless. I suggest you invest in a clockwork alarm clock.