Question

Write nuclear equations to represent (a) the decay of \(^{214} \mathrm{Ra}\) by \(\alpha\) -particle emission (b) the decay of \(^{205}\) At by positron emission (c) the decay of \(^{212} \mathrm{Fr}\) by electron capture (d) the reaction of two deuterium nuclei (deuterons) to produce a nucleus of \(\frac{3}{2} \mathrm{He}\). (e) the production of \({243}_{97} \mathrm{Bk}\) get by the \(\alpha\) -particle bombardment of\({241}_{95} \mathrm{Am}\) (f) a nuclear reaction in which thorium-232 is bombarded with \(\alpha\) particles, producing a new nuclide and four neutrons.

Short answer

The nuclear equations corresponding to the tasks are respectively: \n(a) \(^{214}_{88}\mathrm{Ra} \rightarrow ^{210}_{86}\mathrm{Rn} + ^{4}_{2}\mathrm{He}\), \n(b) \(^{205}_{85}\mathrm{At} \rightarrow ^{205}_{84}\mathrm{Po} + ^{0}_{1}\mathrm{e^{+}}\), \n(c) \(^{212}_{87}\mathrm{Fr} + ^{0}_{-1}\mathrm{e^-} \rightarrow^{212}_{86}\mathrm{Rn}\), \n(d) \(^{2}_{1}\mathrm{H} + ^{2}_{1}\mathrm{H} \rightarrow ^{3}_{2}\mathrm{He} + ^{1}_{0}\mathrm{n}\), \n(e) \(^{241}_{95}\mathrm{Am} + ^{4}_{2}\mathrm{He} \rightarrow^{245}_{97}\mathrm{Bk}\) and \n(f) \(^{232}_{90}\mathrm{Th} + ^{4}_{2}\mathrm{He} \rightarrow^{232}_{92}\mathrm{U} + 4^{1}_{0}\mathrm{n}\).

Step-by-step solution

Nuclear equation for alpha decay of Radon-214

In alpha decay, an alpha particle, which is a helium nucleus (\(^{4}_2\mathrm{He}\)), is emitted. Therefore, the original nucleus loses 2 protons and 2 neutrons. The equation for this reaction is \(^{214}_{88}\mathrm{Ra} \rightarrow ^{210}_{86}\mathrm{Rn} + ^{4}_{2}\mathrm{He}\).

Nuclear equation for positron emission of Astatine-205

In positron emission, a particle with the same mass as an electron but with a positive charge is released. This corresponds to one proton changing into a neutron. The equation for this reaction is \(^{205}_{85}\mathrm{At} \rightarrow ^{205}_{84}\mathrm{Po} + ^{0}_{1}\mathrm{e^{+}}\).

Nuclear equation for electron capture by Francium-212

During electron capture, an electron from the electron shell of the atom is captured by the nucleus, converting a proton into a neutron. The equation for this reaction is \(^{212}_{87}\mathrm{Fr} + ^{0}_{-1}\mathrm{e^-} \rightarrow^{212}_{86}\mathrm{Rn}\).

Nuclear equation for Deuteron-Deuteron Fusion

In a fusion reaction, two or more smaller nuclei combine to form a larger nucleus. The equation for this reaction is \(^{2}_{1}\mathrm{H} + ^{2}_{1}\mathrm{H} \rightarrow ^{3}_{2}\mathrm{He} + ^{1}_{0}\mathrm{n}\).

Nuclear equation for Alpha-particle bombardment of Americium-241

In a reaction with alpha particle bombardment, the target nucleus absorbs the alpha particle. The equation for this reaction is \(^{241}_{95}\mathrm{Am} + ^{4}_{2}\mathrm{He} \rightarrow^{245}_{97}\mathrm{Bk}\).

Nuclear equation for a nuclear reaction with Thorium-232

The equation for this reaction (where Thorium-232 is bombarded with an alpha particle, producing a new nuclide and four neutrons) is \(^{232}_{90}\mathrm{Th} + ^{4}_{2}\mathrm{He} \rightarrow^{232}_{92}\mathrm{U} + 4^{1}_{0}\mathrm{n}\).

Key concepts

Alpha Decay

Alpha decay is a type of radioactive decay where an atomic nucleus ejects an alpha particle. An alpha particle is essentially a helium nucleus, containing 2 protons and 2 neutrons. This decay process results in the transformation of the original atom into a new atom that is lighter by 4 atomic mass units and has a reduction of 2 in its atomic number.

For example, when Radium-214 undergoes alpha decay, it emits an alpha particle and is transformed into Radon-210. The nuclear equation for this process is:
\[ ^{214}_{88}\mathrm{Ra} \rightarrow ^{210}_{86}\mathrm{Rn} + ^{4}_{2}\mathrm{He} \]
This equation shows that the new element Radon has 2 fewer protons than Radium and is correspondingly lighter.

Positron Emission

Positron emission is a decay process where a positron is emitted from an unstable nucleus. A positron has the same mass as an electron but carries a positive charge. This decay occurs when there are too many protons in a nucleus, making it unstable.
To simplify, when a proton transforms into a neutron, a positron is emitted to conserve charge.

The nuclear equation for positron emission in Astatine-205 can be expressed as:
\[ ^{205}_{85}\mathrm{At} \rightarrow ^{205}_{84}\mathrm{Po} + ^{0}_{1}\mathrm{e^{+}} \]
Here, a proton in Astatine changes to a neutron, and the emission of a positron results, creating Polonium-205.

Electron Capture

Electron capture is a process where an inner atomic electron is captured by the nucleus, leading to the conversion of a proton into a neutron. This generally happens when an atom is proton-rich and needs to increase its neutron-proton ratio.
During this capture, the atomic number decreases by one, as a proton is transformed, but the mass number remains unchanged.

An example of electron capture is seen in Francium-212, which captures an electron and converts into Radon-212. The equation that describes this is:
\[ ^{212}_{87}\mathrm{Fr} + ^{0}_{-1}\mathrm{e^-} \rightarrow ^{212}_{86}\mathrm{Rn} \]
This illustrates a proton changing into a neutron with the help of the captured electron.

Nuclear Reactions

Nuclear reactions involve the alteration of an atomic nucleus, resulting in new elements or isotopes. Unlike chemical reactions, which involve electrons, nuclear reactions alter the number of protons or neutrons in a nucleus, leading to more significant energy changes.
One kind of nuclear reaction is the bombardment of nucleons, such as in the reaction of Americium-241 with an alpha particle to create Berkelium-245.

The nuclear equation for this process is:
\[ ^{241}_{95}\mathrm{Am} + ^{4}_{2}\mathrm{He} \rightarrow^{245}_{97}\mathrm{Bk} \]
This shows the alpha particle combining with Americium, resulting in a new isotope of Berkelium.

Deuterium Fusion

Deuterium fusion is a form of nuclear fusion involving deuterium, a heavier isotope of hydrogen with one proton and one neutron. During fusion, two deuterium nuclei combine to form a larger nucleus, such as helium-3, with the simultaneous release of energy.

This type of fusion is represented by the following equation:
\[ ^{2}_{1}\mathrm{H} + ^{2}_{1}\mathrm{H} \rightarrow ^{3}_{2}\mathrm{He} + ^{1}_{0}\mathrm{n} \]
Fusion processes are the power source for stars, including our sun, where such reactions release vast amounts of energy. This energy production occurs as light nuclei merge, creating heavier nuclei and releasing binding energy.