   Chapter 6, Problem 83SCQ

Chapter
Section
Textbook Problem

The radioactive element technetium is not found naturally on Earth; it must be synthesized in the laboratory. It is a valuable element, however, because it has medical uses. For example, the element in the form of sodium pertechnetate (NaTcO4) is used in imaging studies of the brain, thyroid, and salivary glands and in renal blood flow studies, among other things. (a) In what group and period of the periodic table is the element found? (b) The valence electrons of technetium are found in the 5s and 4d subshells. What is a set of quantum numbers (n, l, and ml) for one of the electrons of the 5s subshell? (c) Technetium emits a y-ray with an energy of 0.141 MeV. (1 MeV = 106 electron-volts, where 1 eV = 1.6022 × 10−19 J.) What are the wave- length and frequency of a γ-ray photon with an energy of 0.141 MeV? (d) To make NaTc04, the metal is dissolved in nitric acid. 7 HNO3(aq) + Tc(s) → HTcO4(aq) + 7 NO2(g) + 3 H2O(l) and the product, HTcO4, is treated with NaOH to make NaTcO4. (i) Write a balanced equation for the reaction of HTcO4 with NaOH. (ii) If you begin with 4.5 mg of Tc metal, what mass of NaTcO4 can be made? What mass of NaOH, in grams, is required to convert all of the HTcO4 into NaTcO4? (e) If you synthesize 1.5 micromoles of NaTcO4, what mass of compound do you have? If the compound is dissolved in 10.0 mL of solution, what is the concentration?s

(a)

Interpretation Introduction

Interpretation: The group and period of technetium has to be identified.

Concept introduction:

Periodic Table: The available chemical elements are arranged considering their atomic number, the electronic configuration and their properties. The elements placed on the left of the table are metals and non-metals are placed on right side of the table.

In periodic table the horizontal rows are called periods and the vertical column are called group. There are seven periods and 18 groups present in the table and some of those groups are given special name as follows,

Group1AlkalimetalGroup2AlkalinemetalGroup16ChalcogensGroup17HalogensGroup18Noblegases

Explanation

The atomic number of technetium is 43. The electronic configuration is [Kr]4d55s2

(b)

Interpretation Introduction

Interpretation: The possible set of quantum number for 5s subshell of technetium is to be determined.

Concept introduction:

Quantum numbers are numbers, which explains the existence and the behavior of electron in an atom.

1. a) Principle quantum number is represented by n and this number describes the energy of the orbital and the size of an atom.
2. b) Angular momentum quantum number (or azimuthal quantum number) is represented by l and this number indicates the shape of the orbitals.
3. c) Magnetic quantum number is represented by ml and this number indicates the orientation of the orbital.
4. d) Spin quantum number is represented by ms and this number indicates the spin of the electron.

Principle quantum number is represented by n and this number describes the energy of the orbital and the size of an atom.

The values of l when the principal quantum number is n are from 0 to (n1). Each l value indicates subshell.

The values of ml when the orbital angular quantum number is l are from l to +l.

(c)

Interpretation Introduction

Interpretation: The wavelength and frequency of the γ-ray emitted by technetium has to be calculated.

Concept introduction:

• Planck’s equation,

E=where, E=energyh=Planck'sconstantν=frequency

The energy increases as the wavelength of the light decrease. Also the energy increases as the frequency of the light increases.

• The frequency of the light is inversely proportional to its wavelength.

ν=cλwhere, c=speedoflightν=frequencyλ=wavelength

(d)

Interpretation Introduction

Interpretation:. The balanced equation of the reaction between HTcO4 and NaOH has to be determined. The mass of NaTcO4 produced and NaOH converted have to be calculated.

Concept introduction:

• Chemical equation is the representation of a chemical reaction where the reactants and products of the reactions are represented on left and right side of an arrow respectively by using their respective chemical formulas. It follows conservation law of mass where the number of atoms of each element is equal for reactants and products.
• The number of moles of any substance can be determined  using the equation,

Numberofmole=GivenmassofthesubstanceMolarmass

(e)

Interpretation Introduction

Interpretation: Mass and the concentration of NaTcO4 has to be calculated if it is dissolved in 10.0mL solution.

Concept introduction:

• Molarity (M): Molarity is number of moles of the solute present in the one liter of the solution.

Molarity (M) =Numberofmolesofsolute1literofsolution

• The number of moles of any substance can be determined  using the equation,

Numberofmole=GivenmassofthesubstanceMolarmass

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