Have you wondered why the mass difference between C-11, C-12, and C-13 varies? 🔍🤔
Understanding Isotopes Mass Differences
When it comes to carbon isotopes like C-11, C-12, and C-13, there are intriguing differences in their masses that pique curiosity.
The Role of Neutrons
– The variance in mass between isotopes is primarily due to the different number of neutrons each contains.
– Carbon-11 has 5 neutrons, C-12 has 6 neutrons, and C-13 has 7 neutrons, impacting their overall mass.
Nuclear Stability
– Isotopes with a more balanced ratio of protons to neutrons tend to be more stable.
– This stability affects their mass and varying nuclear properties.
Delving Deeper
By exploring the unique composition and properties of carbon isotopes, it becomes clear why their mass differences are not the same. Keep delving into the fascinating world of nuclear science! 🔬 #CarbonIsotopes #MassDifferences #NuclearScience
Fun enough, you’ve stumbled upon the source of nuclear power – atoms weigh less than the sum of their parts. Also, making my life easy, you chose the easiest atom to discuss it by, because C12 is the atom we use to “baseline” the weights of atomic parts.
As you noticed, C12 weighs exactly 12 u (this says more about our definition of 1u than anything inherently special about Carbon. It’s just the atom we used to set the value of ‘u’). However, both the [proton](https://www.wolframalpha.com/input?i=mass+of+a+proton+in+u) and the [neutron](https://www.wolframalpha.com/input?i=mass+of+a+neutron+in+u) weigh more than 1 u. So, if you add up the weight of the protons and neutrons in a C12 atom, you will see that it “should” weigh [~12.1 u](https://www.wolframalpha.com/input?i=6*%28mass+of+proton+%2B+mass+of+neutron%29+in+u).
This is called the [mass defect or deficit](https://en.wikipedia.org/wiki/Nuclear_binding_energy#Mass_defect) and it is what the famous E = mc^2 equation represents: The decrease in mass is equal to the energy emitted in the reaction of an atom’s creation divided by c^(2).
Now, what you are seeing is that adding each neutron doesn’t add the same amount of mass to the atom. That is because certain isotopes are more stable than others (that is, they have a larger mass defect, or another way, they have more energy binding them together than other isotopes). In both cases, adding a neutron adds less than 1.08 u, which is the mass of a neutron, but you can see going from C11 to C12 the difference is more extreme – you have more of a mass defect so that means going from 11 to 12 is bigger step than going from 12 to 13 in binding energy.
This also leads to why sometimes fusion releases energy (combining 2 atoms into 1 atom), and other times fission releases energy (splitting one atom into two). The stability of an atom isn’t quite based on the total binding energy of the atom, but instead it’s the binding energy per nucleon (a nucleon just being a proton or a neutron, the things that make up the nucleus). If you look up the masses of different atoms, and compare them to the masses of the nucleons that make them up, you will find that the mass defect goes up as you combine light atoms into heavier ones all the way up to Iron, and that the mass defect goes up as you split heavy atoms into smaller ones all the way down to iron.
That is why solar fusion smashes hydrogen atoms into helium (and the process continues [all the way to iron](https://en.wikipedia.org/wiki/Alpha_process)), and why when we do fission we start with heavy atoms, like Uranium.