Question

Predict the type of radioactive decay process for the following radionuclides: (a) \({ }_{5}^{8} \mathrm{~B}\), (b) \({ }_{29}^{68} \mathrm{Cu}\), (c) phosphorus32, (d) chlorine-39.

Short answer

The types of radioactive decay for the given radionuclides are: (a) Beta-plus decay or electron capture, (b) Beta-minus decay, (c) Beta-minus decay, (d) Beta-minus decay.

Step-by-step solution

Identify the neutron to proton ratio of each radionuclide

For each radionuclide, we will calculate the neutron to proton ratio. We can do that by subtracting the atomic number (number of protons) from the mass number (number of protons + neutrons). (a) \({ }_{5}^{8} \mathrm{~B}\): Neutrons = 8 - 5 = 3; n/p ratio = 3/5 (b) \({ }_{29}^{68} \mathrm{Cu}\): Neutrons = 68 - 29 = 39; n/p ratio = 39/29 (c) Phosphorus-32 (\({ }_{15}^{32} \mathrm{~P}\)): Neutrons = 32 - 15 = 17; n/p ratio = 17/15 (d) Chlorine-39 (\({ }_{17}^{39} \mathrm{~Cl}\)): Neutrons = 39 - 17 = 22; n/p ratio = 22/17

Predict the type of radioactive decay based on the n/p ratio and location in the periodic table

Now, we use the neutron-to-proton ratio to determine the type of radioactive decay. (a) \({ }_{5}^{8} \mathrm{~B}\): n/p ratio is 3/5, which is less than 1, meaning that there are more protons than neutrons. Since the element is light and the atomic number is less than 83, we can expect beta-plus decay (emission of a positron) or electron capture. (b) \({ }_{29}^{68} \mathrm{Cu}\): n/p ratio is 39/29, which is greater than 1, meaning that there are more neutrons than protons. Since the atomic number is less than 83, we can expect beta-minus decay (emission of an electron). (c) Phosphorus 32 (\({ }_{15}^{32} \mathrm{~P}\)): n/p ratio is 17/15, which is slightly greater than 1, meaning that there are a few more neutrons than protons. Since the atomic number is less than 83, we can expect beta-minus decay (emission of an electron). (d) Chlorine-39 (\({ }_{17}^{39} \mathrm{~Cl}\)): n/p ratio is 22/17, which is slightly greater than 1, meaning that there are a few more neutrons than protons. Since the atomic number is less than 83, we can expect beta-minus decay (emission of an electron). In conclusion, the types of radioactive decay for the given radionuclides are: (a) Beta-plus decay or electron capture, (b) Beta-minus decay, (c) Beta-minus decay, (d) Beta-minus decay.