In 2002 , a team of scientists from Russia and the United States reported the creation of the first atom of element 118 , which is named oganesson, and whose symbol is Og. The synthesis involved the collision of californium- 249 atoms with accelerated ions of an atom which we will denote X. In the synthesis, an oganesson-294 is formed together with three neutrons. $$ { }_{98}^{249} \mathrm{Cf}+\mathrm{X} \longrightarrow{ }_{118}^{294} \mathrm{Og}+3{ }_{0}^{1} \mathrm{n} $$ (a) What are the identities of isotopes X? (b) Isotope \(X\) is unusual in that it is very long-lived (its half-life is on the order of \(10^{19} \mathrm{yr}\) ) in spite of having an unfavorable neutron-to-proton ratio (Figure 21.1). Can you propose a reason for its unusual stability? (c) Oganesson-294 decays into livermorium-290 by alpha decay. Write a balanced equation for this.

Step by step solution

01

Identify isotope X and its atomic numbers

We are given the following reaction: \({ }_{98}^{249} \mathrm{Cf}+\mathrm{X} \longrightarrow{ }_{118}^{294}\mathrm{Og}+3{ }_{0}^{1} \mathrm{n}\) In order to determine the identity of the isotope X, we must first identify its atomic and mass numbers. Let us denote its atomic number as \(Z\) and its mass number as \(A\). Since the reaction obeys the conservation of mass and atomic numbers, we can set up the following equations: \(98 + Z = 118\) \(249 + A = 294 + 3\)

02

Solve for atomic and mass numbers of isotope X

Now, we can solve these equations to find the atomic and mass numbers for isotope X: \(Z = 118 - 98 = 20\) \(A = 294 + 3 - 249 = 48\) Thus, isotope X has an atomic number of 20 and a mass number of 48.

03

Identify the element and isotope of X

Now that we have the atomic and mass numbers for isotope X, we can identify the element and its isotope. An element with an atomic number of 20 is calcium (Ca), so isotope X is calcium-48 or \({}_{20}^{48}\mathrm{Ca}\). (a) The identity of isotope X is calcium-48 (\({}_{20}^{48}\mathrm{Ca}\)).

04

Discuss the unusual stability of isotope X

Isotope X, calcium-48, has a very long half-life (on the order of \(10^{19}\) years) despite having an unfavorable neutron-to-proton ratio. This unusual stability can be attributed to its magic numbers of protons and neutrons. A nucleus is said to have magic numbers when the number of protons and/or neutrons leads to a closed shell configuration, resulting in increased stability. In the case of calcium-48, it has 20 protons and 28 neutrons, which are both magic numbers. (b) Calcium-48 has magic numbers of protons and neutrons, leading to a closed shell configuration and increased stability.

05

Write the balanced equation for the alpha decay of oganesson-294

Oganesson-294 decays into livermorium-290 through alpha decay. In alpha decay, an alpha particle (consisting of 2 protons and 2 neutrons) is emitted from the nucleus. Therefore, we can write the balanced nuclear equation as follows: \({}_{118}^{294} \mathrm{Og} \longrightarrow{ }_{116}^{290}\mathrm{Lv} + { }_{2}^{4}\mathrm{He}\) (c) The balanced equation for the alpha decay of oganesson-294 into livermorium-290 is: \({}_{118}^{294} \mathrm{Og} \longrightarrow{ }_{116}^{290}\mathrm{Lv} + { }_{2}^{4}\mathrm{He}\)

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