Problems on isotopes
Level A
1. Calculate the isotopic composition (in%) of hydrogen (average relative atomic mass A r = 1.008) and lithium (A r = 6.9), assuming that each element consists of only two isotopes whose relative atomic masses differ by one.
Answer. Hydrogen: 1 H – 99.2% and 2 H – 0.8%; lithium: 6 Li – 10% and 7 Li – 90%.
2. The relative atomic mass of natural hydrogen is 1.00797. This hydrogen is a mixture of protium isotopes ( A r = 1.00782) and deuterium (A r = 2.0141). What is the percentage of deuterium in natural hydrogen?
Answer. 0,015%.
3. Among the given symbols of elements, indicate isotopes and isobars:
Answer. Isotopes have the same chemical symbols, and isobars have the same atomic masses.
4. Natural lithium (A r = 6.9) consists of isotopes with mass numbers 6 and 7. What percentage of the first isotopedoes it contain?
Answer. 10%.
5. The mass of an atom of the magnesium isotope is 4.15 10 –23 d. Determine the number of neutrons that the nucleus of this atom contains.
Answer. 13.
6. Copper has two isotopes with mass numbers 63 and 65. Mass fraction their content in natural copper is 73% and 27%, respectively. Based on these data, calculate the average relative atomic mass of natural copper.
Answer. 63,54.
7. The average relative atomic mass of natural chlorine is 35.45. Calculate the mass fractions of two of its isotopes having mass numbers 35 and 37.
Answer. 77.5% and 22.5%.
8. Determine the relative atomic mass of boron if the mass fractions of its isotopes are known ( 10 B) = 19.6% and( 11 B) = 80.4%.
Answer. 10,804.
9. Lithium consists of two natural isotopes with mass numbers 6 ( 1 = 7.52%) and 7 ( 2 = 92.48%). Calculate the relative atomic mass of lithium.
Answer. 6,9248.
10. Calculate the relative atomic mass of cobalt if it is known that two of its isotopes exist in nature: with mass numbers 57 ( 1 = 0.17%) and 59 ( 2 = 99,83%).
Answer. 58,9966.
11. The relative atomic mass of boron is 10.811. Determine the percentage of isotopes with mass numbers 10 and 11 in natural boron.
Answer. 18.9% and 81.1%.
12. Gallium has two natural isotope with mass numbers 69 and 71. What is the quantitative relationship between the numbers of atoms of these isotopes if the relative atomic mass of the element is 69.72.
Answer. 1,78:1.
13. Natural bromine has two isotopes with mass numbers 79 and 81. The relative atomic mass of bromine is 79.904. Determine the mass fraction of each isotope in natural bromine.
Answer. 54.8% and 45.2%.
Level B
1. Silicon has three stable isotopes – 30 Si (3.05%(mol.)), 29 Si and 28 Si. Calculate the content (in % (mol.)) of the most common isotope of silicon. How will they differ? molar masses silicon dioxide, which has a different isotopic composition, considering that oxygen has three stable isotopes with mass numbers 16, 17 and 18?
Answer. 94.55%; 18 types of silicon dioxide molecules.
2. The sample consists of a mixture of two isotopes of one element; 30% is an isotope, the nucleus of which has 18 neutrons; 70% is an isotope whose atomic nucleus contains 20 neutrons. Determine the atomic number of an element if the average relative atomic mass of the element in a mixture of isotopes is 36.4.
Answer. 17.
3. A chemical element consists of two isotopes. The nucleus of an atom of the first isotope contains 10 protons and 10 neutrons. There are 2 more neutrons in the nucleus of an atom of the second isotope. For every 9 atoms of a lighter isotope there is one atom of a heavier isotope. Calculate the average relative atomic mass of the element.
Answer. 20,2.
4. Isotope 137 Cs has a half-life of 29.7 years. 1 g of this isotope reacted explosively with excess water. What is the half-life of cesium in the resulting compound? Justify your answer.
Answer. T 1/2 = 29.7 years.
5. After how many years does the amount of radioactive strontium-90 (half-life 27 years) fall out as a result of radioactive fallout? nuclear explosion, will become less than 1.5% of the amount that was discovered at the moment after the nuclear explosion?
Answer. 163.35 years.
6. In the tagged atom method, radioactive isotopes are used to “trace the route” of an element in the body. Thus, a patient with a diseased pancreas is injected with a preparation of the radioactive isotope iodine-131 (undergoes – -decay), which allows the doctor to monitor the passage of iodine through the patient’s body. Write an equation for radioactive decay and calculate how long it takes for the amount of radioactive iodine introduced into the body to decrease by 10 times (half-life 8 days).
Answer.
7. How long will it take for three quarters of the nickel to turn into copper as a result of – -decay, if the half-life of the isotope 63 28 Ni is 120 years old?
Answer. 240 years.
8. Find the mass of the isotope 81 Sr (half-life 8.5 hours) remaining after 25.5 hours of storage if the original mass was 200 mg.
Answer. 25 mg.
9. Calculate the percentage of isotope atoms 128 I (half-life 25 minutes), remaining undisintegrated after storage for 2.5 hours.
Answer. 1,5625%.
10. Half life – -radioactive isotope 24 Na is equal to 14.8 hours. Write the equation for the decay reaction and calculate how many grams of the daughter product are formed from 24 g of this isotope in 29.6 hours.
Answer.
11. Isotope 210 Ro, radiating-particles, used in a mixture with beryllium in neutron sources. After what time will the intensity of such sources decrease by 32 times? The half-life of the isotope is 138 days.
Answer. 690 days
Exercises on nuclear reactions
1. How many- And – -particles had to lose their nucleus 226 Ra to obtain a daughter element with mass number 206, belonging to group IV periodic table elements? Name this element.
Answer. 5, 4 – , 206 82 Pb.
2. Nucleus of an isotope atom 238 92 U turned into a nucleus as a result of radioactive decay 226 88 Ra. How many- And – -particles were emitted by the original nucleus?
1. Which element has more pronounced non-metallic properties: a) at oxygen or carbon; b) phosphorus or arsenic? Give a reasoned answer based on the position of the elements in periodic table.
2. Give a description of element No. 11 according to the plan:
Position on the periodic table
Metal or non-metal
Atomic structure
Electronic formula
Number of electrons on the outer energy level whether it is complete
Superior Oxide Formula
Does the element form volatile compound with hydrogen, if it forms, what is its chemical formula
3. How and why properties change chemical elements in periods? Show this using the example of elements of the 3rd period.
4. Calculate the relative atomic mass of boron if it is known that the proportion of the 10 B isotope is 19.6%, and the 11 B isotope is 80.4%. (Answer: 10.8.)
Solutions and answers:
1. Non-metallic properties are more pronounced in a) oxygen (since from left to right in periods non-metallic properties increase),
b) phosphorus (since in groups from bottom to top, non-metallic properties are enhanced due to a decrease in the radius of the atom).
3. In periods from left to right, non-metallic properties increase and metallic properties weaken, because Due to the increase in the number of electrons in the valence shell, the electrons begin to be more strongly attracted to the nucleus, and the radius of the atom decreases.
From the lesson materials you will learn that the atoms of some chemical elements differ from the atoms of other chemical elements in mass. The teacher will tell you how chemists measured the mass of atoms that are so small that you cannot see them even with the help of electron microscope.
Topic: Initial chemical ideas
Lesson: Relative Atomic Mass of Chemical Elements
At the beginning of the 19th century. (150 years after the work of Robert Boyle), the English scientist John Dalton proposed a method for determining the mass of atoms of chemical elements. Let's consider the essence of this method.
Dalton proposed a model according to which a molecule of a complex substance contains only one atom of different chemical elements. For example, he believed that a water molecule consists of 1 hydrogen atom and 1 oxygen atom. Included simple substances according to Dalton, only one atom of a chemical element is included. Those. an oxygen molecule must consist of one oxygen atom.
And then, knowing the mass fractions of elements in a substance, it is easy to determine how many times the mass of an atom of one element differs from the mass of an atom of another element. Thus, Dalton believed that the mass fraction of an element in a substance is determined by the mass of its atom.
It is known that the mass fraction of magnesium in magnesium oxide is 60%, and the mass fraction of oxygen is 40%. Following the path of Dalton's reasoning, we can say that the mass of a magnesium atom more mass oxygen atom by 1.5 times (60/40=1.5):
The scientist noticed that the mass of the hydrogen atom is the smallest, because there is no complex substance in which the mass fraction of hydrogen would be greater mass fraction another element. Therefore, he proposed to compare the masses of atoms of elements with the mass of a hydrogen atom. And in this way he calculated the first values of the relative (relative to the hydrogen atom) atomic masses of chemical elements.
The atomic mass of hydrogen was taken as unity. And the meaning relative mass sulfur turned out to be equal to 17. But all the values obtained were either approximate or incorrect, because the experimental technique of that time was far from perfect and Dalton’s assumption about the composition of the substance was incorrect.
In 1807 - 1817 Swedish chemist Jons Jakob Berzelius conducted extensive research to clarify the relative atomic masses of elements. He managed to obtain results close to modern ones.
Significantly later work Berzelius began to compare the masses of atoms of chemical elements with 1/12 of the mass of a carbon atom (Fig. 2).
Rice. 1. Model for calculating the relative atomic mass of a chemical element
The relative atomic mass of a chemical element shows how many times the mass of an atom of a chemical element is greater than 1/12 the mass of a carbon atom.
Relative atomic mass is denoted by A r; it has no units of measurement, since it shows the ratio of the masses of atoms.
For example: A r (S) = 32, i.e. a sulfur atom is 32 times heavier than 1/12 the mass of a carbon atom.
Absolute mass 1/12 of a carbon atom is a reference unit, the value of which is calculated with high accuracy and is 1.66 * 10 -24 g or 1.66 * 10 -27 kg. This reference mass is called atomic unit masses (a.e.m.).
There is no need to memorize the values of the relative atomic masses of chemical elements; they are given in any textbook or reference book on chemistry, as well as in the periodic table of D.I. Mendeleev.
When calculating, the values of relative atomic masses are usually rounded to whole numbers.
The exception is the relative atomic mass of chlorine - for chlorine a value of 35.5 is used.
1. Collection of problems and exercises in chemistry: 8th grade: to the textbook by P.A. Orzhekovsky and others. “Chemistry, 8th grade” / P.A. Orzhekovsky, N.A. Titov, F.F. Hegel. – M.: AST: Astrel, 2006.
2. Ushakova O.V. Chemistry workbook: 8th grade: to the textbook by P.A. Orzhekovsky and others. “Chemistry. 8th grade” / O.V. Ushakova, P.I. Bespalov, P.A. Orzhekovsky; under. ed. prof. P.A. Orzhekovsky - M.: AST: Astrel: Profizdat, 2006. (p. 24-25)
3. Chemistry: 8th grade: textbook. for general education institutions / P.A. Orzhekovsky, L.M. Meshcheryakova, L.S. Pontak. M.: AST: Astrel, 2005.(§10)
4. Chemistry: inorg. chemistry: textbook. for 8th grade. general education institutions / G.E. Rudzitis, Fyu Feldman. – M.: Education, OJSC “Moscow Textbooks”, 2009. (§§8,9)
5. Encyclopedia for children. Volume 17. Chemistry / Chapter. ed.V.A. Volodin, Ved. scientific ed. I. Leenson. – M.: Avanta+, 2003.
Additional web resources
1. Unified collection of digital educational resources ().
2. Electronic version of the journal “Chemistry and Life” ().
Homework
p.24-25 No. 1-7 from Workbook in chemistry: 8th grade: to the textbook P.A. Orzhekovsky and others. “Chemistry. 8th grade” / O.V. Ushakova, P.I. Bespalov, P.A. Orzhekovsky; under. ed. prof. P.A. Orzhekovsky - M.: AST: Astrel: Profizdat, 2006.
1. Natural magnesium consists of the isotopes 24Mg, 25Mg and 26Mg. Calculate the average atomic mass of natural magnesium if the content of individual isotopes in percent by mass is respectively 78.6; 10.1 and 11.3.
2. Natural gallium consists of the isotopes 71Ga and 69Ga. What is the quantitative relationship between the numbers of atoms of these isotopes if the average atomic mass of gallium is 69.72.
3. Determine the relative atomic mass of boron if it is known that the mole fraction of the 10B isotope is 19.6%, and the 11B isotope is 80.4%.
4. Copper has two isotopes: 63Cu and 65Cu. Their molar fractions in natural copper are 73 and 27%, respectively. Determine the average relative atomic mass of copper.
5. Determine the relative atomic mass of the element silicon if it consists of three isotopes: 28Si (mole fraction 92.3%), 29Si (4.7%) and 30Si (3.0%).
6. Natural chlorine contains two isotopes 35Cl and 37Cl. The relative atomic mass of chlorine is 35.45. Determine the mole fraction of each isotope of chlorine.
7. The relative atomic mass of neon is 20.2. Neon consists of two isotopes: 20Ne and 22Ne. Calculate the mole fraction of each isotope in natural neon.
8. Natural bromine contains two isotopes. The molar fraction of the 79Br isotope is 55%. What other isotope is included in the element bromine if its relative atomic mass is 79.9.
9. Natural thallium is a mixture of isotopes 203Tl and 205Tl. Based on the relative atomic mass of natural thallium Ar(Tl) = 204.38, determine the isotopic composition of thallium in % by mass.
10. Natural iridium is a mixture of isotopes 191Ir and 193Ir. Based on the relative atomic mass of natural iridium Ar(Ir) = 192.22, determine the isotopic composition of iridium in % by mass.
11. Natural rhenium is a mixture of 185Re and 187Re isotopes. Based on the relative atomic mass of natural rhenium Ar(Re) = 186.21, determine the isotopic composition of rhenium in % by mass.
12. Natural gallium is a mixture of isotopes 69Ga and 71Ga. Based on the relative atomic mass of natural gallium Ar(Ga) = 69.72, determine the isotopic composition of gallium in % by mass.
13. Natural chlorine consists of two stable isotopes 35Cl and 37Cl. Based on the average relative atomic mass of chlorine of 35.45, calculate the isotopic composition of chlorine as a percentage by mass.
14. Natural silver consists of two stable isotopes 107Ag and 109Ag. Based on the average relative atomic mass of silver of 107.87, calculate the isotopic composition of silver as a percentage by mass.
15. Natural copper consists of two stable isotopes 63Cu and 65Cu. Based on the average relative atomic mass of copper of 63.55, calculate the isotopic composition of copper as a percentage by mass.
16. Natural bromine consists of two stable isotopes 79Br and 81Br. Based on the average relative atomic mass of bromine of 79.90, calculate the isotopic composition of bromine as a percentage by mass.
17. Natural silicon consists of 3.1% (by moles) of the isotope 30Si (with an atomic mass of 29.9738), as well as the isotopes 29Si (with an atomic mass of 28.9765) and 28Si (with an atomic mass of 27.9770). Calculate the content in % (by moles) of 29Si and 28Si.
