Final answer:
In the transmutation of Boron-12 to Carbon-12, the emitted radiation is a beta particle, causing the atomic number to increase by one and changing the element's identity from Boron to Carbon.
Step-by-step explanation:
The type of nuclear radiation emitted in the transmutation of Boron-12 to Carbon-12 is a beta particle emission. During beta decay, a neutron in the nucleus is transformed into a proton and an electron. The electron, which is the beta particle, is then ejected from the nucleus. The atomic number increases by one while the atomic mass number remains the same, indicating the identity of the element has changed (from Boron to Carbon in this case). This process does not involve the emission of alpha particles or neutrons, and gamma rays are usually emitted in conjunction with the beta particle but are not the main product of the transformation.