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

Hi everyone. This problem reads below is an image showing 30 atoms of a hypothetical element az the blue spheres correspond to Az with a mass of 190.3 units. Meanwhile the green spheres correspond to 193 A Z. With a mass of 193.4 units, calculate the atomic mass of AZ. So in order for us to calculate the atomic mass, we're going to need to know the relative abundance of both 198 and 193. And once we have those relative abundances we can multiply them by their mass units to get the atomic total mass. So let's go ahead and start there. So for our relative abundance I'll initial that as our a for 190 A Z. We know that's represented by the blue spheres. And so we have 22 blue spheres out of 30 total. Okay. And we're going to multiply that by 100. So our relative abundance for the 1 90 Az is 73.3%. So let's go ahead and do the same thing for R 93 az. Okay. We're going to calculate its relative abundance and we have eight green spheres out of 30 total and we're going to multiply this by 100 And that gives us 26.67%. Okay, Let me rewrite that. So it's a little clearer. 26.67%. So now that we know the relative abundance of each, we can calculate the atomic mass. Okay. And we're going to calculate the atomic mass by taking the relative abundance and multiplying it by its mass units. So for our 1 90 az our relative abundance as a decimal is 0. times its units. Its mass units is 190. units. And this is going to be added to our 1 Az we know its mass percent is a relative abundance is 0.2267 times its unit mass units is 100 and 93.4 units. Okay, so in total we get 191. Units and this is going to be our atomic mass. So let me write that a little clearer. I apologize. So we get .23 units. And this is going to be our final answer. We'll move this to the side. So there we go. That's it for this problem. I hope this was helpful

Ch.2 - Atoms, Molecules, and Ions

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Brown 14th Edition

Ch.2 - Atoms, Molecules, and Ions

Problem 2b

Chapter 2, Problem 2b

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?

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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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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.