Can I detect nuclear explosions with coherer?
You could detect the impulse that way, yes.

You would do better to use a diode of some sort, though.

Any society capable of building an A-Bomb is also capable of building a diode and a better detector.
A-Bombs have a fair amount of electronics in them for the detontation mechanism - the shaped charges have to be set off at the correct time in the correct sequence to get an explosion instead of a fizzle (big, messy release of radiation without the Kaboom.)



Lightning strikes will also activate this kind of detector, as well as better ones made from diodes.

What you have is practically an untuned AM receiver.  Just run the antenna straight to the detector with no tuning elements (capacitors or inductors.)

There are schematics available on the internet for lightning detectors of various kinds - from simple to fairly sophisticated.  Have a look at some of them.  Most of them include an amplifier of some kind.

Here's a lightning detector made with a coherer.


Note that the hammer for the bell is arranged to smack the bell when the coherer is activated, and to smack the coherer on release. The solenoid for the hammer is arranged to break its own current path when activated - it turns itself off automatically.

This is a MUST because an activated coherer won't release by itself - once current start flowing, it will continue to do so.  Smacking it causes the particles to realign and the resistance goes back up again.

Also note that coherers are mechanically delicate.  They are made of a glass envelope with a powder inside.  They are physically whacked every time they are used, and will tend to break eventually.



I assume you are thinking in terms of "world building" for a story of some kind.
It might be reasonable for a more primitive society to use coherers to detect A-Bomb explosions caused by a more advanced society.
It would not be reasonable for a society capable of building A-Bombs to use coherers to detect the explosions.