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Published: Friday, 19 September 2025 22:10

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Nuclear chemistry

This is the study of reactions involving nucleus of atoms. So far, all chemical reactions that we saw occurred with electrons revolving around the nucleus. However, here reaction takes place within nucleus of atoms, which releases energy orders of magnitude more than what chemical reactions involving electrons release.

Libretext Link => https://chem.libretexts.org/Bookshelves/Introductory_Chemistry/Introduction_to_General_Chemistry_(Malik)/08%3A_Nuclear_chemistry/8.01%3A_Introduction_to_nuclear_chemistry

Khan Academy (6 excellent intro videos)=> https://www.youtube.com/playlist?list=PLSQl0a2vh4HCBNsg2hoAn0ZpFrmNbX4XO

Isotopes:

We saw in periodic table section that number of protons is unique to an element. But how about number of neutrons, is that unique too? Turns out, that number of neutrons for an atom of an element can change, but the chemical properties are almost the same. Such variation of elements which have atoms with different number of neutrons are called isotopes of that element. It's very hard to distinguish b/w Isotopes of an element, as spectroscopy (which depends on electron's energy levels) will give same spectral lines for diff isotopes. Their chemical and physical properties are almost indistinguishable, except for their mass. Isotopes may be stable (don't decay due to radioactivity) or unstable (decay over time due to radioactivity).

Mass Spectrometry: To separate out isotopes of an element, a special equipment/ called Mass spectrometer is used (mass is used in definition implying it measures mass via spectrometry). Lower mass isotopes are deflected more than ones with higher mass.

Nuclide is a term similar to isotope where it refers to atom whose nucleus has specified number of protons and neutrons. For ex: Carbon-13 is a nuclide or isotope of Carbon with 6 protons and 7 neutron (number 13 refers to atomic mass number A). Carbon-13 is also written as ¹³
₆C
where 13 on top refers to A and 6 on bottom refers to Z. We need both numbers A and Z in defining an element uniquely, since if we omit A, then we can't diff b/w isotopes. The term nuclide is used since nuclear properties of these isotopes vary a lot, depending on the number of neutrons in nucleus. A total of 3339 nuclides is known of which 339 are naturally occurring, and remaining 3000 have been created artificially. Of these 339, 286 have existed since creation of solar system,  with 251 being stable nuclides and remaining 35 with very long half life of > 100M years. So, that leaves us with 53 (339-286=53) naturally occurring isotopes which are radioactive. Stable isotopes are the only ones we talk about at lower Z. Unstable isotopes occur at high Z (starting from polonium with Z=84). They are studied in detail in nuclear chemistry.

Wiki: https://en.wikipedia.org/wiki/Isotope

Hydrogen is the only element whose isotopes show most diff in chemical properties primarily due to the fact that the 3 isotopes of Hydrogen differ by weight in ratio of 1:2:3, so that starts affecting the chemical reactions, as much heavier isotopes of an atom have lower reactivity than lighter isotopes of same element. When we go to high Z elements, the extra number of neutrons don't cause weight to go up by 2X or 3X, so their extra weight effect is much more muted in chemical reactions.

When we look atomic weight (NOT atomic mass number) of elements in periodic table, we see that none of them are integer values, even though they are expressed in amu. How is that possible, since number of protons or neutrons is an integer number? The reason is that atomic weight of any element is the weighted avg of all naturally occurring isotopes of that element (since that is how atomic weights were determined historically. Pure samples of that element were taken and weights calculated, which contained isotopes of that element in same proportion as what was found in nature). About 80 elements in periodic table have stable isotopes. There's a chart in link above that shows the plot of N(# of neutrons) vs Z (# of protons). For lower Z, N is usually same or 1 more than Z. Generally the ratio of N:Z keeps going higher as Z increases, since more neutrons are needed to bind the nucleus together when more protons are present (needed to keep protons further apart and lower their repulsive forces, which is possible if we insert more neutrons b/w them which attract not only other neutrons but other protons too).

Ex: Berillium has 2 isotopes with N=3 and N=4 (i.e atomic mass=6 amu with 7.5% concentration and 7 amu with 92.5% concentration). This gives avg amu as = 6*0.075+7*0.925=6.92 which is close to the amu reported in the periodic table. Similarly for all other elements.

Magic Numbers (MN): Whether an isotope is stable or not is determined by the number of protons and neutrons in nucleus. We saw the bank of stability in above wiki link. There is a trend observed with elements Helium, Oxygen, Calcium, Nickel, Tin, Lead and hypothetical Unbihexium. Their isotopes are highly stable because they have magic number of protons or neutrons in their nucleus. MN is a number of nucleons (either protons or neutrons, separately) such that they are arranged into complete shells within the nucleus. The seven most widely recognized magic numbers as of 2019 are 2, 8, 20, 28, 50, 82, and 126. 

Doubly Magic: Nuclei which have neutron numbers and proton numbers both equal to one of the magic numbers are called "doubly magic", and are generally very stable against decay. The known doubly magic isotopes are Helium-4, Helium-10, Oxygen-16, Calcium-40, Calcium-48, Nickel-48, Nickel-56, Nickel-78, tin-100, tin-132, and lead-208.

Wiki => https://en.wikipedia.org/wiki/Magic_number_(physics)

Lbretext => https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Nuclear_Chemistry/Nuclear_Energetics_and_Stability/Nuclear_Magic_Numbers

Nuclear power => https://www.nuclear-power.com/nuclear-power/reactor-physics/atomic-nuclear-physics/nuclear-stability/

All isotopes try to get closer to the band of stability by undergoing decay. This decay is called radioactive or nuclear decay and the unstable atom loses energy and emits out energy in form of ionizing radiation, thus reducing the internal energy of the new nucleus which makes it more stable (as lower energy state implies higher stability).

• Alpha decay: Nuclides which have Z>82 are at top of plotted kine and unstable. which have  decay by emitting an alpha particle which is just a He Nucleus. This reduces N by 2 and Z by 2, effectively changing the element to something else, but making it more stable in the process (as the new element gets closer to stable band). Helium nucleus is released, as it's extremely stable nucleus. Most of the Helium on earth comes from this radioactive decay of elements found inside the core of earth. This alpha decay is also what keeps the earth's core so hot. Some energy is released as KE of both nuclides, so nuclides internally have less energy making them more stable. These alpha particles don't have any electrons in them, so they are +ve charged. As such, they are highly ionizing, but they have very low penetration power (can be easily stopped by a piece of paper). Alpha particles have have short range and low energy.
  • ex of Alpha decay:   ²³⁸
    ₉₂U
     ->  ²³⁴
    ₉₀Th
     +  ⁴
    ₂He 
    
  • Alpha decay is used in smoke detectors. Since +ve charged He nuclides ionize the air particles around them, causing a conducting current. When smoke is present, this ionizing ability of He nuclide is highly disrupted, causing a drop in current. 
• Beta Decay: Nuclides which have lower mass (usually Z < 82) decay via beta decay. Beta decay results in beta particles being emitted, which are much lighter (as they are just electrons or anti electrons). So, beta particles can travel longer (being lighter than alpha particle). Beta decay have more energy and more range than alpha decay. There are 2 types of beta decay.
  • Beta β^- Decay: Nuclides which have very high number of neutrons compared to protons (lying above the band of stability) decay by changing neutron to proton. The increases Z by 1 and decreases N by 1. This also changes the element. An anti-neutrino is also released in the process, as it accounts for slight energy that was missing.
    • ex of β^- decay:   ¹⁴
      ₆C
       ->  ¹⁴
      ₇N  +  ⁰
      _-1e  + ȳ_e  (anti-neutrino particle)
  • Positron β⁺ Decay:  Nuclides which have very low number of neutrons compared to protons (lying below the band of stability) decay by releasing protons (i.e positron). Positron is called anti-matter of electron. The decreases Z by 1 bringing Z closer to N. Similar to β^- Decay, a neutrino is also released in the process, as it accounts for slight energy that was missing. Electron capture is another way to decay where an electron is captured in the nuclei, basically reducing Z by 1. This results in release of X-ray, and is different than positron decay, but achieves the same result.
    • ex of β⁺ decay:   ¹³
      ₇N
       ->  ¹³
      ₆C +  ⁰
      ₊₁e + γ_e (neutrino particle)
  • Beta decay is used in controlling thickness of paper in industry. This is because beta particles pass thru paper easily (you need plastic or glass to stop beta particle), and depending on thickness, varying amount of beta particles pass.
• Gamma decay: Gamma decay happens with alpha or beta decay. The daughter nuclide formed after an alpha/beta decay may be in excited state, where the neutrons/protons are in higher energy state. This is where high energy photons, called as gamma rays, are released from an excited nucleus in high energy state to bring it to a low energy state. Gamma rays are most energetic and have high frequency. Gamma rays have most penetrating power (even more than X-rays). Few inches of lead is needed to stop gamma rays. All 3 radiations are ionizing radiations, but gamma has the least ionizing power, as they are neutral in charge. Alpha/beta decay is followed by gamma decay.
  • ex of gamma decay: First beta decay occurs => β^- decay:   ⁶⁰
    ₂₇Co
     ->  ⁶⁰
    ₂₈Ni^* +  ⁰
    _-1e  + ȳ_e (anti-neutrino particle). * indicated excited state of Ni.
  • Now, gamma decay occurs to bring this excited Ni^* to Ni. Gamma decay => ⁶⁰
    ₂₈Ni^* ->  ⁶⁰
    ₂₈Ni  + ϒ (gamma)
  • All alpha, beta and gamma radiations are dangerous, but gamma is least ionizing. This is used in tumor surgery to destroy tumors, as they have most penetrating power (they can reach deep inside our body). They destroy tumors by targeting g=multiple gamma rays. 

Half Life => Radio active elements decay at a constant rate, i.e some % of matter decays in a given time. We define Half life as the amount of time it takes for the material to decay to half of it's original amount.

ex: Half life of U-238 is 4.5 Billion years. So, if we start with 100 g of U-238, then after 4.5B years, we'll be left with 50g. Further 4.5B years, we'll have 25 g remaining and so on.

Estimating age of Earth => Zircon crystals hate Pb, and have Uranium in them. So, any trace of Pb that we find in Zircon crystal, should have come from Uranium radioactivity. So, based on proportion of U vs Pb, we can determine the age of zircon.

Estimating age of fossils => Carbon 14 dating is used. Carbon 14 has half life of 5700 years. When a living being is alive, it continually consumes Carbon, which is all 3 isotopes in same proportion as what appears in nature. However, once that living being dies, the carbon is no longer ingested, and hence the only carbon remaining is whatever carbon isotopes were at death. Now C-14 being radioactive starts decaying, so the ratio of C-14 to C-12 tells us how long it has been since the organism died. 

Nuclear Energy (NE):

Under "phases of matter" section, we saw internal energy, ionization energy and nuclear energy. Forming of nucleus itself involves releasing a lot of energy, so that it can achieve a lower energy state. For Hydrogen-1, which has only 1 proton, there's no nuclear energy (as soon as we take out an electron from aHydrogen-1, single proton becomes free, there's nothing more to further break down into smaller particles). 

To recapture, below are mass of proton and neutron. 1 amu = 1.66053886 × 10^-27 kg

• Proton mass: 1.67262192 × 10^-27 kg  = 1.007276 u

• Neutron mass: 1.674927471 × 10^-27 kg = 1.008665 u

Mass of proton and neutron is fixed, irrespective of which atoms they go in. However when we measure weight of a nuclei in any atom, it's always less than the sum of individual protons and neutrons. The missing weight is the one that gets converted into energy (based on E=m*c^2) and is released.

Now, let's consider H-2 (deuterium), which has 1 proton and 1 neutron in nucleus. 

Total nuclear mass = 1.007276 u+1.008665 u=2.015941 u, while measured mass =  2.014102 u. So, some mass is missing, which is the mass that got converted into energy.

Since 1 atomic mass unit =931.494 MeV/c2, Nuclear binding energy = Eb = Δm*c^2≈0.001839×931.494≈1.71 MeV. Measured nuclear energy = 2.21MeV (energy per nucleon = 2.21/2=1.1 MeV per nucleon). Slight discrepancy is due to rounding of mass of protons and neutrons. This is energy per atom. If we take 1 mole of atoms, NE/mole = 2.21 MeV*6.022*10^23 = 2.21 *10^6 * 1.6*0^-19J * 6.02*10^23 = 200*10^9 = 210 *10^9 J/mole (210 Billion Joule/mole) 

This Nuclear Binding energy is 1000X more than Ionization Energy (IE). This energy is released to form the nuclei, so energy of nuclei is finally -ve. But in Nuclear study, we write nuclear binding energy as +ve. So, we say NE of H-2 (deuterium) is 2.2MeV/atom.

Nuclear Fusion: Here, smaller nuclei combine to form a larger nuclei. This is what happens in Sun's core, where larger atoms are formed from smaller atoms. Fusing nuclei is not easy, as they have to come very very close to each other (within nuclear range), which happens at very high temperature and pressure. It happens within Star's cores where new heavier nucleus get formed , releasing energy. This is the energy we looked at above.

ex:  ¹
₁H +   ²
₁H  ->  ³
₂He  + ϒ (gamma) => Here 2 H atoms fuse to form Helium, along with the release of energy as gamma rays. The difference in mass on 2 sides, gives the amount of energy released using E=m*c^2.

Stars fuse H to form He, then He fuses to form Be and so on. It continues until Fe. Once we reach Fe, fusion stops as Fe is one of the most stable elements which doesn't fuse anymore. It needs energy to fuse Fe, instead of fusion releasing energy. So, once Fe is formed, the star collapses under sheer weight due to gravity, and supernova happens, which blasts all these elements into space, and that's how these elements end up on planets like earth. Earth is basically star dust from such events.

NOTE: nuclear fusion is very hard to do experimentally as it requires very high speed of nucleons along with high Temp and Pressure, which makes it difficult to do in lab.

Nuclear Fission: It's opposite of fusion where larger nuclei break (or fiss) to form multiple smaller nuclei. This happens for elements whose nuclei is not very stable to start with. Usually we bombard these nuclides with a neutron, which makes it even more unstable, which causes the nuclide to break into smaller daughter nuclides along with 1-3 neutrons being ejected.The end products (daughter nuclide) may themselves be radioactive, which may be dangerous to humans. 

Only some nuclides can undergo fission, and they are called fissile.  ²³⁵
₉₂U
 is fissile but  ²³⁸
₉₂U
 is not. So, 1 isotope of U, U-235 is fissile, but other isotope, U-238 isn't. The reason has to do with daughter nuclides are formed, and if they are more stable than the parent nuclide. Most of the Uranium found in nature is U-238 (99.3%), and only small amount is U-235(0.7%). Through a process called enrichment, we increase the concentration of U-235 in the Uranium mix., 

The question that come to mind is to break such nucleus, we need a lot of energy. However for unstable ones, we don't need that much energy, and in process we end up getting some energy. However, the enormous energy that we get in fission is due to chain reactions, which doesn't require us to put in more energy for every atom. 1 atom breaks other atoms due to neutrons released, and so on, releasing lots of energy. The difference in mass on the 2 sides (reactants minus products), gives the Energy released, based on E=m*c^2. Just one fission reaction gives very low energy, but one fission gives rise to exponential number of fissions, and all of them combined give out a lot of energy.

 ex:   ²³⁵
₉₂U
 +  ¹
₀n ->  ⁹⁴
₃₈Sr
 +  ¹⁴⁰
₅₄Xe +  2¹
₀n  => Here U-235 is bombarded with 1 neutron, and it releases 2 neutrons in the process. These 2 neutron will collide with other adjoining nuclides and cause chain reaction.
 

 ex:   ²³⁵
₉₂U
 +  ¹
₀n ->  ⁹²
₃₆Kr
 +  ¹⁴¹
₅₆Xe +  3¹
₀n  => Here U-235 is bombarded with 1 neutron, but it releases 3 neutrons in the process.  So, the chain reaction will go even faster here, as 3 neutrons will hit more adjoining nuclides.

Uses: Nuclear bombs and nuclear plants are based on nuclear fission (and NOT on nuclear fusion). In nuclear bomb, the chain reaction is uncontrolled, but in nuclear power plant, the chain reaction is controlled, allowing only controlled number of neutrons from each chain reaction (by absorbing extra neutrons). In uncontrolled fission, 90% of U is enriched, but in controlled fission, only 3-5% is enriched, which limits the rate at which chain reaction can take place