The nationwide RadNet system monitors the nation's air to track radiation in the environment. Over time, RadNet sample testing and monitoring results show the fluctuations in normal background levels of environmental radiation. The RadNet system will also detect higher than normal radiation levels during a radiological incident.
I don't know if they have an API but there is a way to download parts of their data as CSV files.
Interactive query builder: https://radnet.epa.gov/radnet-public/query.do
Wikiversity course material about radiation, electromagnetism, and the physics thereof.
A crowdsourced open environmental data project. volunteer centered. Measures airquality, radiation, and environmental health.
Another crowdsourced radiation monitoring website.