Is nuclear power safe? Not 100% safe, no. Perfect safety does not exist. Nothing is without risk. Therefore, to allow you to properly assess "safety" I've provided a few facts you might not be aware of.
How many people died from Chernobyl, the world's deadliest nuclear disaster? You are probably thinking "thousands", but the actual number is 70. Surprised? Certainly there were health effects after the disaster. Among children exposed at the time of the accident, about 4000 cases of thyroid cancer were reported (the survival rate for this cancer is 92% after 30 years). Incidents of other diseases and birth defects did rise statistically. However there were no discernible long-term effects. Per a UNSCEAR report:
...there is no evidence of a major public health impact attributable to radiation exposure 20 years after the accident. There is no scientific evidence of increases in overall cancer incidence or mortality rates or in rates of non-malignant disorders that could be related to radiation exposure. The risk of leukemia in the general population, one of the main concerns owing to its short latency time, does not appear to be elevated. Although those most highly exposed individuals are at an increased risk of radiation-associated effects, the great majority of the population is not likely to experience serious health consequences as a result of radiation from the Chernobyl accident.Note that this is a worst-case incident. There was NO containment vessel at Chernobyl. At Three-Mile Island, where a containment vessel was used, there were zero casualties.
Let's assume that all 4000 cases of thyroid cancer resulted in death. Surely this would make nuclear power the most deadly form of power! But no, it turns out that digging out the coal for our coal-fired power plants is far more costly in human lives. In the past century, over 100,000 coal miners were killed in the United States alone, and many more died from black lung and other health effects.
In addition to the human cost, coal-fired plants release more radiation into the atmosphere than an operating nuclear plant. This is because some of the trace elements found in coal are naturally radioactive. These include uranium, thorium, radium and radon. In the worse-case, residents around a coal-fired plant may receive 1 to 5 percent higher background radiation than they would otherwise see.
As I said, NOTHING is without risk.