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The odds of radioactivity giving you new organs is on the order of the probability of you spontaneously generating new limbs without radiation. It's so slim we don't even think about it.

The growth of an organ is an astonishingly orchestrated art. Dozens of small factors come together in an environment which is conducive to organ generation. There's all sorts of fun things going on. For example, the nerves from the optic nerve in the eye grow backwards along chemical trails to the visual cortex in the rear of the brain. Those chemical trails cease to exist afterwards. The retina then produces a unique test pattern of ever widening diamonds which the visual cortex then uses to sort through the signals to figure out which nerves go where. After this very short phase in development, you will never see that test pattern again; the retina never again emits it.

As an analogy for what you seek, consider the orchestra hit at the beginning of Star Wars. Its bright, beautiful, and it sets the mood for the rest of the movie. In theory, one could hand a pile of instruments to a bunch of 5 year olds, and they could reproduce that sound. But, more than likely, the sound will be more like what you expect from a bunch of 5 year olds handed musical instruments. A cacophony.

That cacophony is called cancer.

Indeed, the difference between an organ and cancer is that we like what the organs do, and they formed at an agreed upon reasonable time.

If you want a fun lesson on how this works, take a look at Caenorhabditis elegans. It's a nemoatode which has been studied in depth. We actually understand all of the genetic and environmental signals which go into the construction of its nervous system. It's pretty glorious!

If you really want exotic mutations due to radiation, it will have to be something other than the radiation that causes it. Perhaps the species you are dealing with has a very particular defensive mechanism against inhospitable environments, and a touch of radiation is sufficient to trigger it. Then it's not the radiation that's causing an organ to form, it's some pre-chosen pattern in the DNA which responds to stresses.

When DNA manipulation techniques were yet to come, and scientists wanted to explore genetic mutation, they had to use something similar to what you depicted. They applied this method to developing new plant variants.

How did it work?

They placed a gamma emitter in the center of a circular field, then planted crops all around.

During growth the crops were exposed to different level of gamma radiation, and developed various random mutations. The produced, mutated seeds were then planted on a normal field and the plants tested for useful mutations.

This is how some of the currently most diffused wheat varieties have been developed.

While this can be applied to plants, it's hardly transferrable to animals/humans:

• plants produce hundreds to thousands seeds each time. Animals at best
  can have ten babies per time. Humans hardly go past 1. Since you are playing with statistics, big numbers are your friend here.


• plants, especially crops used for farming, reproduce once a year and within one season. Humans cannot reproduce earlier than about 12 years from birth. Again, big numbers are your friends.


• plants do not have specific body plans and organs, while animals do. Parts of a plant growing chaotically will generally not harm the rest of the plant, while this will kill animals. (credits @IndigoFenix for pointing it out)

In any case, to grow new organs as a consequence of mutation, you need:

• a mutation in the right place in the genetic code


• the mutation must be active when that part of the genetic code is used

Now, in our genetic code, the part about developing limbs and organs is expressed during the embryo growth, then it is silenced. Therefore mutating that part after the growth, as it would happen for an adult exposed to radiation, would be useless. It's like changing the recipe of a cake after you have baked it: it won't bear any consequence on the cake.

The only mutations we know that triggers cellular growth are those leading to cancer, which, as you might now, is all but an organized growth.

No

To mutate, the person needs to be a fetus at the time and the odds are extremely low. In all likelihood the fetus would self abort from the cellular damage.

Radiation can damage the DNA but that leads to cancer or just dying of radiation poisoning.

As several other people have suggested, exposure to radiation is extremely unlikely to do anything except make you sick in a variety of ways, including cell death and cancer among a depressing list of bad.

It is just barely possible that your offspring would grow an extra organ of the same type as an existing one. An extra toe is not an extremely rare thing. This is basically a "counting" error, and could exist without killing the individual. Three kidneys instead of two, and things such as that. When such things do happen they often produce non-functional versions. The extra toe has no muscles or tendons attached. The extra kidney has no connections to the urinary system. So even this is often a significant detriment to the individual.

An entirely new organ is grossly unlikely. Organs don't simply spring into existence without a development history. You get slight changes that are then selected in or out of the gene pool, depending on if they are slightly better or worse than the rest of the population.

However, the people on this planet might only think it was radiation. They might be subject to neoteny. The axolotl is a salamander-like critter that lives in water. Ordinarily it goes through its entire life cycle in water, living, breeding, raising young, etc. If they get injected with iodine then they metamorphose into a different form that is more adapted to living on land. Seems like some distant ancestor of this critter was so adapted, and they lost that stage at some point. But it's still there lurking in their DNA. And a big dose of iodine can bring it out.

So maybe these people are neotonous. At some point in their evolutionary history they had a metamorphosis to adapt to some condition. Maybe it was much wetter part of the year. But they lost this adaptation. Maybe a massive dose of something in the plants will trigger the growth of gills to allow them to live in ponds. There are lots of possibilities.

However, this would not be random. There would be a certain condition that triggered a certain transformation. Possibly incomplete in some individuals who had not got the full set of transformed genes. But it would not occasionally produce some entirely unknown thing. Creatures that were neotonous forms of salamanders would not suddenly grow feathers and wings, for example.

Radiation, no. Too random. But hey, we're not talking about humans here, so let's play with this... in spite of the science-based tag, probably.

In our own world we have numerous examples of multi-stage life forms that pass through two or more forms after birth to adulthood. Tadpoles grow legs and lose their tails to become frogs. Dragonfly nymphs moult several times, the last time revealing their wings. Eels go through up to 4 different metamorphoses during their life cycle. And so on.

Interestingly, not all animals capable of metamorphosis do so purely on biological timers. Sometimes the transformation only occurs due to environmental factors.

Let's assume that some time in the ancient past of your world the proto-humanoids were just such a creature. They start out as a vaguely ape-shaped creature and remain that way until they encounter the environmental factor that stimulates a gland to produce the hormones that start their transformation to adulthood. The stimulus is fairly common in plants of their world, but over time they evolve to a nearly symbiotic relationship on a particular family of plants. Only by consuming the sap of the plants in that family will their final transformation begin.

As their transformation stimulus becomes more specific they also evolve to become fully fertile during their 'juvenile' stage. They no longer need to transform to continue their species. This new strain is less reliant on the plants because they can breed without them. They continue to develop until the local equivalent of H. Sap. becomes the dominant intelligent species of the planet.

But somewhere in their heads there is a tiny group of cells, a small gland that looks like part of their endocrine system but doesn't seem to have any real purpose. Nobody really knows what it does.

Until one day some explorer finds a small plant with an interesting smell and starts eating it. He falls ill of course, and when the fevers pass he has changed. Maybe he has new parts, maybe some of those old parts that everyone thought were just atavistic left-overs from their evolutionary past become enlarged and fully functional again. Their endocrine balance shifts and so on.

So he gives the plant to someone else and it kills them, because their genetics are too far off the original line. In fact it turns out that only a small percentage of the population actually has suitable genetics to survive the transformation process, he was just one lucky S.O.B.

70% are lacking the genetic sequence that codes for iodothyronine (or whatever hormone you like) production or some other blocker and nothing happens. 20% go through the transformation with varying degrees of success, including the few full transformations.

And the other 10%, unlucky sods that they are, die in screaming agony as the transformation goes out of control and destroys their bodies.

So... 1 in 10 chance of agonizing death.

Et voila, an 'intelligent' species with a reason to do something stupid that's probably going to do nothing but could make them much better than other people. Or kill them horribly.

No radiation required. :)

It is not possible to grow new organs by exposure to radioactivity. Radiation is harmful and in strong enough doses it kills.

It would require something like genetic engineering to grow new organs. In fact, the human beings in your story would need to have acquired something like the ability of the axolotl and other animals, which mostly are reptilian, to grow new or replacement organs when damaged or injured.

This assumes the people in your world will have been modified by genetic engineering at some time in the past. Certainly long enough ago that rituals concerning the growth of new organs have developed and are part of their society.

The plants capable triggering the growing of new organs may contain chemicals or molecular biological agents that cause their bodies to commence new organ growth. Agents of this kind may have been inserted in the plants by genetic engineering.

This scenario assumes there were persons (aliens?? time-travellers??) who possessed genetic engineering technology. They could have modified both the people and plants in your world. Rituals of growing new organs could have been encouraged to exist by them or the rituals may have arisen through natural interaction by the world's people with the plants.

Feel free to suggest alternative or solution to grow new organs like mutant or through eating other stuff (the people don't necessary biologically/anatomically like human except they are bipedal before mutation), if exposure or eating radioactive can't grow limbs or new organs.

Since others have already answered the question I thought I could give an interesting alternative!

There are parasitic worms that are known to cause extreme limb mutations in frog species. Such as giving the host many additional legs. This mutation however occurs while the frog transforms from tadpole to mature, so it is unlikely to work on already mature humans.

You can find more here:
https://en.wikipedia.org/wiki/Ribeiroia