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Chapter 2: Problem 96

Copper (Cu) consists of two naturally occurring isotopes with masses of 62.9296 and 64.9278 u. (a) How many protons and neutrons are in the nucleus of each isotope? Write the complete atomic symbol for each, showing the atomic number and mass number. (b) The average atomic mass of Cu is $63.55 \mathrm{u}$. Calculate the abundance of each isotope.

Short Answer

Expert verified
The two naturally occurring isotopes of Copper, \(_{29}^{63}\textrm{Cu}\) and \(_{29}^{65}\textrm{Cu}\), have 29 protons and 34 or 36 neutrons in their nucleus, respectively. The abundance of each isotope is 69.18% for \(_{29}^{63}\textrm{Cu}\) and 30.82% for \(_{29}^{65}\textrm{Cu}\).

Step by step solution

01

Find the atomic number of Copper (Cu)

Copper is a chemical element, and its atomic number can be found in the periodic table. In the periodic table, Copper is represented by the symbol Cu and has an atomic number of 29.
02

Determine the number of protons and neutrons in each isotope

Since the atomic number of Copper is 29, it means that Copper has 29 protons in its nucleus. For the first isotope with mass 62.9296 u, the number of neutrons can be found as follows: Number of neutrons = mass number - atomic number = 63 (rounded) - 29 = 34 neutrons For the second isotope with mass 64.9278 u, the number of neutrons can be found as follows: Number of neutrons = mass number - atomic number = 65 (rounded) - 29 = 36 neutrons
03

Write the complete atomic symbol for each isotope

The complete atomic symbol for each isotope can be written as: Isotope 1: \(_{29}^{63}\textrm{Cu}\) (29 protons and 34 neutrons) Isotope 2: \(_{29}^{65}\textrm{Cu}\) (29 protons and 36 neutrons)
04

Calculate the abundance of each isotope using the average atomic mass

Let x be the abundance of isotope 1 (\(_{29}^{63}\textrm{Cu}\)) and (1-x) be the abundance of isotope 2 (\(_{29}^{65}\textrm{Cu}\)). The sum of the product of each isotope mass and its abundance should equal the average atomic mass of Copper, which is given as 63.55 u. 62.9296 * x + 64.9278 * (1-x) = 63.55 Now, we solve for x: x = (63.55 - 64.9278) / (62.9296 - 64.9278) = 0.6918 Thus, the abundance of isotope 1 (\(_{29}^{63}\textrm{Cu}\)) is 69.18%, and the abundance of isotope 2 (\(_{29}^{65}\textrm{Cu}\)) is 100 - 69.18 = 30.82%.

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Most popular questions from this chapter

Bromine has two naturally occurring isotopes, bromine- 79 (atomic mass \(=78.9183 \mathrm{u} ; \quad\) abundance \(=50.69 \%)\) a \(\mathrm{nd}\) bromine-81 \(\quad\) (atomic mass \(=80.9163 \mathrm{u} ;\) abundance \(=\) $49.31 \%) .$ Calculate the atomic weight of bromine.

Write the chemical formulas for the following compounds: (a) aluminum hydroxide, \((\mathbf{b})\) potassium sulfate, \((\mathbf{c})\) copper(I) oxide, \((\mathbf{d})\) zinc nitrate, \((\mathbf{e})\) mercury(II) bromide, (f) iron(III) carbonate, \((\mathbf{g})\) sodium hypobromite.

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