Atomic Numbers and Multiplying Fractions

The Atomic

Number, Z, of an element

is the number of protons

within the nucleus of the

element's atom. This

leads to some interesting

arithmetic!

A portion of the

Periodic Table of the

elements is shown to the

left with the symbols and

atomic numbers for each

element indicated in each

square.

Problem 1 - Which element has an atomic number that is 5 1/3 larger than carbon (C)?

Problem 2 - Which element has an atomic number that is 5 2/5 that of neon (Ne)?

Problem 3 - Which element has an atomic number that is 8/9 that of krypton (Kr)?

Problem 4 - Which element has an atomic number that is 2/5 of astatine (At)?

Problem 5 - Which element has an atomic number that is 5 1/8 that of sulfur (S)?

Problem 6 - Which element has an atomic number that is 3 2/3 that of fluorine (F)?

Problem 7 - Which element in the table has an atomic number that is both an even

multiple of the atomic number of carbon, an even multiple of the element magnesium

(Mg) which has an atomic number of 12, and has an atomic number less than iodine (I)?

Space Math http://spacemath.gsfc.nasa.gov

Answer Key

Problem 1 - Which element has an atomic number that is 5 1/3 larger than Carbon (C)?

Answer: Carbon = 6 so the element is 6 x 5 1/3 = 6 x 16/3 = 96/3 = 32 so Z=32 and the

element symbol is Ge (germanium).

Problem 2 - Which element has an atomic number that is 5 2/5 that of Neon (Ne)?

Answer: Neon = 10, so 10 x 5 2/5 = 10 x 27/5 = 270/5 = 54, so Z=54 and the element is

Xe (xenon).

Problem 3 - Which element has an atomic number that is 8/9 that of Krypton (Kr)?

Answer: Krypton=36 so 36 x 8/9 = 288/9 = 32, so Z=32 and the element is Ge

(germanium).

Problem 4 - Which element has an atomic number that is 2/5 of Astatine (At)? Answer;

Astatine=85 so 85 x 2/5 = 170/5 = 34, so Z=34 and the element is Se (selenium).

Problem 5 - Which element has an atomic number that is 5 1/8 that of Sulphur (S)?

Answer; Sulphur = 16 so 16 x 5 1/8 = 16 x 41/8 = 82, so Z=82 and the element is lead

(Pb).

Problem 6 - Which element has an atomic number that is 3 2/3 that of Fluorine (F)?

Answer: Fluorine = 9 so 9 x 3 2/3 = 9 x 11/3 = 99/3 = 33, so Z=33 and the element is

As (arsenic).

Problem 7 - Which element in the table has an atomic number that is both an even

multiple of the atomic number of carbon, an even multiple of the element magnesium

(Mg) which has an atomic number of 12, and has an atomic number less than Iodine (I)?

Answer: The first relationship gives the possibilities: 6, 18, 36, 54. The second clue

gives the possibilities 36 and 84. The third clue says Z has to be less than I = 53, so

the element must have Z = 36, which is Kr, (krypton).

Space Math http://spacemath.gsfc.nasa.gov