When a radioactive isotope releases a beta particle, the atomic number of the new element is

A. decreased by one.
B. decreased by two.
C. increased by one.
D. increased by two.

You can figures these out if you remember that a beta particle has a -1 charge and a mass number of 0 and you think about it. In radioactive reactions the subscripts must add up and the superscripts must add up. Here is an example. It's difficult to write subscripts and superscripts on this forum so the first number I write will be the atomic number (number of protons and second number will be the mass number (number of nucleons).

11Na23 ==> -1eo + ?X?. The -1eo is the beta particle. Just add everything as above to get this. For the subscripts we have
11 = -1 + ? so ? must be 12.
For the superscripts we have
23 = 0 + ? so ? must be 23. Look up element number 12 on the periodic table to find X and find it is Mg so the equation is
11Na23 ==> -1eo + 12Mg23
A disclaimer. I don't know that 11Na23 does this; il.e., it's and example only to you how it works.

To determine the atomic number of the new element when a radioactive isotope releases a beta particle, we need to understand that a beta particle is a high-energy electron or positron that is emitted from the atomic nucleus during radioactive decay.

In beta decay, a neutron in the nucleus of the radioisotope is converted into a proton, resulting in the emission of a beta particle. A proton has an atomic number of 1, while a neutron has no charge and no atomic number. Therefore, when a neutron is transformed into a proton, the atomic number of the nucleus increases by one.

Based on this explanation, the correct answer is:

C. increased by one.