Substantial exposure to ionising radiation can cause immediate damage to the body, e.g. skin burns, cataracts and sterility. Sources in museum collections are unlikely to be this dangerous. However, there is no established safe level of exposure to radiation and even at low levels repeated or prolonged exposure may increase the risks of cancer, infertility and genetic defects.
Exposure can occur from outside the body. A person receives a dose simply by being near to a radioactive source. Museum objects are more likely to be a hazard internally via ingestion or inhalation of radioactive materials or gases such as radon.