Isotopes

Atoms with the same number of protons,

but different numbers of neutrons.

Atoms of the same element (same atomic

number) with different mass numbers

Isotopes of chlorine

35Cl 37Cl17 17

chlorine - 35 chlorine - 37

Natural abundances of isotopes

Natural chlorine contains :

75 % 35Cl and 25 % 37Cl . 17 17

• These percentages are known as the natural abundances of the isotopes and determined by “mass spectrometry.”

Average atomic mass/average mass/atomic mass/ atomic

weight• Is the weighted mean.

amu5.35100

)37x25()35x75(

Exercise 1

• The atomic mass of iridium is 192.2 g / mol. What are the naturally occurring percentages of the two isotopes of Ir-191 and Ir-193?

solution

40x

2.192100

)x100(193)x(191

Iridium is a mixture of 40% 191Ir and 60 % 193Ir.

Isotopes of Hydrogen element

H

H

H

11

21

31

has the biggest abundance in nature.

Tritium

Deuterium

• A mass spectrometer is an instrument which separates particles according to their masses , records the relative proportions of these, and determine natural abundances of the isotopes of an element. Therefore, it also allows us to calculate the atomic mass of an element.

• The most accurate way for determining atomic and molecular weights is provided by mass spectrometer.

Mass spectrometry

• mass spectrometer, invented by the English physicist Francis William Aston (1877-1945) when he was working in Cambridge with J. J. Thomson. It was in his use of this instrument that the existence of isotopes of elements was discovered.

• Aston eventually discovered many of the naturally occurring isotopes of non-radioactive elements.

• He was awarded the Nobel Prize for Chemistry in 1922.

Mass spectrometry

Mass spectrometry

A B

C

DE

accelerating

F

A: a gaseous sample is very slowly

introduced to the mass spectrometer.

B: atoms/molecules are bombarded by a stream of high energy electrons to produce positive ions, mostly w/ a 1+ charge. These electrons collide w/ electrons in the particle knocking them out and leaving a positive ion.

C: positively charged ions are accelerated high enough to make the particles pass through the slits and magnetic field by high electrical voltage on the negatively charged grid. With the slits, the ions were made a beam of ions.

D: Fast moving ions enter a magnetic field

produced by an electromagnet. Ions are deflected by a magnetic field into a curved path. The deflection of the ions depends on “charge to mass ratio(q/m). ”The more massive the ion, the less the deflection. The ions w/ equal mass and charge will deflect the same.

E: By changing the strength of the magnetic field or the accelerating voltage on the negatively charged grid, ions of varying masses can be made to enter the detector at the end of the instrument.

• On the detector, ions are collected on a

metal plate and the current flows through the metal plate to neutralise the ions and this current is recorded.

• In this way, the relative abundances of ions of different masses in the sample can be determined and put into a graph called “mass spectrum.”

F: The mass spectrometer must be at a high vacuum for its correct operation and its correct operation depends on particles being able to pass through it w/o colliding with any other particles.

• A: vapourised sample introduced

• B: ionization by electron bombardment

• C: Positive ions accelerated by electrical field

• D: ions deflected by a magnetic field

• E: detector records ions of a particular mass

• F: vacuum prevents molecules colliding

Atomic weight measurements How was the atomic weight measured?• By mass spectrometry

– This also measures

% natural abundance

for a given isotope- The graph is called as

“mass spectrum.”

Atomic weight calculation There are three naturally occuring isotopes

of neon (Ne):

20Ne isotopic mass = 19.99244018 amu21Ne isotopic mass = 20.9938467 amu22Ne isotopic mass = 21.9913855 amu

the atomic weight is reported in text as:20.1797 amu

Masses of Atoms

A scale designed for atoms gives their small

atomic masses in atomic mass units (amu)

An atom of 12C was assigned an exact mass of

12.00 amu

Relative atomic masses of all other atoms was

determined by comparing each to the mass of 12C

An atom twice as heavy has a mass of 24.00

amu (Mg=24.00amu). An atom 12 times lighter

than 1 C-12 atom is 1.00 amu(H=1.00amu).

Atomic mass unit(amu or u or Da)

• 1/12th of the mass of one C-12 atom.

Average atomic mass(atomic weight/average mass/atomic

mass)• “atomic weight or mass” = average

mass of an atom calculated from the masses and natural abundances of all isotopes

Atomic Mass

Average atomic mass is based on all the

isotopes and their abundance %

Atomic mass is not a whole

number!!!!

Na22.99

Calculating Atomic Weight or Mass

Percent(%) abundance of isotopes

Mass of each isotope of that element

Weighted average =

mass isotope1(%) + mass isotope2(%) + …

100 100

• Naturally occurring C is composed of 98.93

% 12C and 1.07 % 13C. The masses of these nuclides are 12 amu (exactly) and 13.00335 amu, respectively.

amu01.12100

)amu00335.13x07.1()amu12x93.98(

Average atomic mass(atomic mass) or atomic weight

Atomic Mass of Magnesium

Isotopes Mass of Isotope Abundance 24Mg = 24.0 amu 78.70%

25Mg = 25.0 amu 10.13%

26Mg = 26.0 amu 11.17%

Atomic mass (average mass) Mg = 24.3 amu

Mg24.3

Atomic mass calculation

How was the atomic mass calculated?

• multiply each isotopic mass by the reported natural abundance for the isotope, then:

• add these individual contributions for each isotope to get the average atomic mass for the element

Atomic mass calculation

There are three naturally occuring isotopes of neon (Ne):20Ne mass # = 19.99244018 amu (90.51%)21Ne mass # = 20.9938467 amu (0.27%)22Ne mass # = 21.9913855 amu (9.22%)

the atomic mass is reported in text as:

20.1797 amu

18.10 + 0.057 + 2.03 = 20.19 amu

Learning Check 5

Gallium is a metallic element found in

small lasers used in compact disc players.

In a sample of gallium, there is 60.2% of

gallium-69 (68.9 amu) atoms and 39.8% of

gallium-71 (70.9 amu) atoms. What is the

atomic mass of gallium?

Solution

Ga-69

68.9 amu x 60.2 = 41.5 amu for 69Ga

100

Ga-71 (%/100)

70.9 amu x 39.8 = 28.2 amu for 71Ga

100

Atomic mass Ga = 69.7 amu

Finding An Isotopic Mass

A sample of boron consists of 10B (mass 10.0 amu) and 11B (mass 11.0 amu). If the average atomic mass of B is 10.8 amu, what is the % abundance of each boron isotope?

Assign X and Y values:X = % 10B Y = % 11B

Determine Y in terms of XX + Y = 100Y = 100 - X

Solve for X:X (10.0) + (100 - X )(11.0) = 10.8

100 100

Multiply through by 10010.0 X + 1100 - 11.0X = 1080

Collect X terms

10.0 X - 11.0 X = 1080 - 1100

- 1.0 X = -20

X = -20 = 20 % 10B

- 1.0

Y = 100 - X

% 11B = 100 - 20% = 80% 11B

Learning Check 6

Copper has two isotopes 63Cu (62.9 amu) and 65Cu (64.9 amu). What is the % abundance of each isotope? (Hint: Check Zumdahl or any other chemistry text for atomic mass)

1) 30% 2) 70% 3) 100%

Solution

2) 70%

Solution

62.9X + 6490 = 64.9X = 6350

-2.0 X = -140

X = 70%

Atomic Masses

13C12C

13.00335 amu (1.11%)

12.0000 amu (98.89%)

atomic weight of C = 12.01115 amu WHY?

Calculating masses of atoms relative to 12C

(mass of 12C atom) * 1.58320 = mass of F atom

= 18.99840

reported atomic weight of F = 18.9984