Which part of iPhone is responsible for radiation
By radiation, I'm assuming you mean the creation of electromagnetic waves and not the movement of sub-atomic particles like X-Rays.
In that case, it would be the transmitter (technically the transceiver since it's an all in one device).  It's the transmitter that generates the electromagnetic waves at their respective frequencies with embedded data through the antennas that creates this radiation.
How a Transmitter Works

There's three components to a transmitter

Oscillator creates the &quot;carrier wave&quot; at a specified frequency.  This is the LTE, GSM or PCS frequencies that your carrier (AT&amp;T, Sprint, Verizon, etc.) uses.

Modulator embeds all of the data onto the wave signal generated by the oscillator

Amplifier (with antenna) takes that signal and increases it's power so that it's strong enough to reach the closest receiver.


Particle Radiation
If you're referring to the movement of sub-atomic particles from your iPhone, there isn't any.  There's no component (like the battery you mentioned) with any degree of radioactivity (This is the &quot;dangerous radiation&quot;).  It would be illegal to sell that to the general public.