The truth is that smoke detectors contain less than a microgram of Am-241. It has a half-life of 432 years. And AmO2 does not burn, volatilize or dissolve in water under any conditions found on Earth's surface, and can't leave your detector and harm you unless you grind it up fine and snort it.

Worry less about radiation from your smoke detector, and more about radiation from bricks (esp mud bricks) and concrete in your home.

And worry less about those and more about every other insult your mind and body are exposed to in today's world, like bad food, bad media and lack of exercise...