There is often much controversy over nuclear power because of the waste that the process generates. How to safely store nuclear waste is in fact so disputed that many people completely disregard the energy source, saying that the method is irresponsible of us to dump on future generations. But what if there was a better way to dispose of nuclear waste...like sending it to the sun?!
While sending nuclear waste to the sun may be technically feasible, the material would burn up in space long before it even reached the sun. And despite that, it's quite unlikely that we'll be pursuing this mission. That's partly because the actual material that would be worth getting rid of in such an extreme way only makes up about 3% of all nuclear waste. When we talk about nuclear waste we're including clothing and tools exposed to radioactivity, not just the radioactive rocks. In fact, in 1999 there was a study that looked at the possibility of space disposal for highly reaction nuclear waste; this came from the calculation that by 2020 there will be 32,946 kg of spent nuclear fuel rods alone on the planet. Sending all that weight into space would be extremely expensive, so it's not quite as plausible as it may seem.
But the even bigger reason why it's unlikely that we'll be sending our nuclear waste to the sun anytime soon is that in order to do so we would have to cancel the Earth's orbital velocity. (That would be necessary in order to ensure that we could accurately target the Sun.) The amount of energy required to do that would be ridiculously high, and thus it's probably a better idea to use that energy for a more certain bet.