Write a balanced nuclear equation for the positron emission of each of the following nuclei: a) arsenic-74
b) oxygen-15
a) The balanced nuclear equation for the positron emission of arsenic-74 can be written as:
^74As -> ^74Ge + 0e+1 + νe
In this equation, ^74As represents the nucleus of arsenic-74, ^74Ge represents the nucleus of germanium-74, 0e+1 represents the emitted positron, and νe represents the emitted neutrino.
b) The balanced nuclear equation for the positron emission of oxygen-15 can be written as:
^15O -> ^15N + 0e+1 + νe
In this equation, ^15O represents the nucleus of oxygen-15, ^15N represents the nucleus of nitrogen-15, 0e+1 represents the emitted positron, and νe represents the emitted neutrino.
To write a balanced nuclear equation for positron emission, we need to understand the process of positron decay and how it affects the atomic and mass numbers of the radioactive nucleus.
Positron emission occurs when a proton in the nucleus is converted into a neutron, and a positron is emitted. The atomic number decreases by 1, and the mass number remains the same.
Now let's write the balanced nuclear equation for each of the given nuclei:
a) Arsenic-74:
In this case, arsenic-74 undergoes positron decay. Arsenic has an atomic number of 33. Since positron emission decreases the atomic number by 1, the resulting nucleus will have an atomic number of 32.
Atomic Number: 33 - 1 = 32
The mass number of arsenic-74 remains unchanged at 74.
Mass Number: 74
Writing the balanced nuclear equation:
^74 As --> ^74 Ge + ^0e
b) Oxygen-15:
Oxygen-15 has an atomic number of 8. Following the principles of positron decay, the resulting nucleus will have an atomic number of 7.
Atomic Number: 8 - 1 = 7
The mass number of oxygen-15, as indicated by the isotope name, remains intact at 15.
Mass Number: 15
Writing the balanced nuclear equation:
^15 O --> ^15 N + ^0e
Overall, positron emission involves the conversion of a proton into a neutron, resulting in a decrease in the atomic number by 1 while the mass number remains constant.
The secret to these is to write an equation in which the subscripts add up on both sides and the superscripts add up on both sides. Subscripts and superscripts are a problem on the board so this is the way I will show it.
8O15 means oxygen with an atomic number of 8 and a mass of 15
33As74 means As with an atomic number of 33 and a mass of 74
A positron is the same as an elecrron but with a positive charge so we write it as 1e0.
8O15 ==> 1e0 + X
So 8 on the reactant side = 1 + something on the product side. What is something? That must be 7 because 7+1 on the product side = 8 on the reactant side.
What about the superscripts; i.e., the numbers on the right. 15 on the reactant side = 0 on the product side + something. That something must be 15 because 15+0 = 15. Now what is element X? The atomic number is 7 so that makes it N. Look at the periodic table to confirm that.