The following diagram is a representation of 20 atoms of a fictitious element, which we will call nevadium (Nv). The red spheres are ²⁹³Nv, and the blue spheres are ²⁹⁵Nv. (b) If the mass of ²⁹³Nv is 293.15 u and that of ²⁹⁵Nv is 295.15 u, what is the atomic weight of Nv?

검증된 단계별 안내

Count the number of red spheres (293Nv) and blue spheres (295Nv) in the diagram.

Calculate the total number of atoms by adding the number of red spheres and blue spheres.

Determine the fraction of each isotope by dividing the number of each type of sphere by the total number of atoms.

Multiply the mass of each isotope by its respective fraction to find the weighted contribution of each isotope to the atomic weight.

Add the weighted contributions of both isotopes to find the atomic weight of nevadium (Nv).

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Atomic Mass Unit (u)

The atomic mass unit (u) is a standard unit of mass that quantifies mass on an atomic or molecular scale. It is defined as one twelfth of the mass of a carbon-12 atom, approximately 1.66 x 10^-27 kg. In this context, the masses of the isotopes of nevadium (293Nv and 295Nv) are given in atomic mass units, which allows for the calculation of the average atomic weight based on their relative abundances.

Isotopes

Isotopes are variants of a chemical element that have the same number of protons but different numbers of neutrons, resulting in different atomic masses. In the case of nevadium, 293Nv and 295Nv are isotopes, with 293Nv having 293 nucleons and 295Nv having 295 nucleons. Understanding isotopes is crucial for calculating the average atomic weight, as it involves considering both the mass and the relative abundance of each isotope.

Average Atomic Weight

The average atomic weight of an element is calculated by taking the weighted average of the atomic masses of its isotopes, based on their relative abundances. This is expressed mathematically as: (mass of isotope 1 × fraction of isotope 1) + (mass of isotope 2 × fraction of isotope 2). In this question, the average atomic weight of nevadium can be determined using the provided masses of 293Nv and 295Nv along with their respective quantities in the diagram.

The following diagram is a representation of 20 atoms of a fictitious element, which we will call nevadium (Nv). The red spheres are 293Nv, and the blue spheres are 295Nv. (b) If the mass of 293Nv is 293.15 u and that of 295Nv is 295.15 u, what is the atomic weight of Nv?