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In Mission Impossible: Fallout, there is a scene where Benjamin Dunn is examining a plutonium core brought by Eastern European gangsters. He touched the core with some sort of a rod and when asked what is that thing? He replies:

This is a Beryllium rod, which is causing a reaction with the plutonium inside the core.

I have 2 related questions.

Is the way Benji detects the plutonium realistic?

I searched the Internet and came across a topic called startup neutron source which I believe a source for initiating a stable nuclear reaction. Here, there is an example of a plutonium/beryllium reaction. Is this the concept used in the movie or is it a fictional method of detection?

Why doesn't he use a simpler device like Geiger counter to measure radioactivity? I am sure it is a lot cheaper and widely available device and can accurately measure radioactivity and confirm radioactive elements.

Is it safe to touch the core with bare hands?

Why are the characters in the movie not making any safety precautions while handling the core. It is presumably radioactive, and you wouldn't want to touch it with bare hands but the characters don't seem to care. Is the core made up of metal that is preventing the radioactive rays from escaping?

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