Chapter U1.13, Problem 3E

Interpretation Introduction

Interpretation: Difference between potassium-39, potassium-40 and potassium- 41 is to be explained and the isotope symbols for three isotopes of potassium are to be written.

Concept Introduction: An atom is made of particles called electrons, protons and neutrons. Atoms of one element are different from atoms of another element. Sometimes atoms of the same element are also different due to the different number of neutrons in them. Isotopes are atoms of the same element with a different number of neutrons.

Answer to Problem 3E

Potassium-39, potassium-40 and potassium- 41 are three isotopes of potassium. They are different in their masses or mass number. Potassium- 39 has an atomic mass of 39 amu or mass number is 39, Potassium- 40 has an atomic mass of 40 amuor mass number is 40, and Potassium- 41 has an atomic mass of 41 amuor mass number is 41. The three isotopes have different numbers of neutrons. Potassium- 39 has 1 neutron less than Potassium- 40 and two neutrons less than Potassium- 41. Potassium- 40 has one neutron less than Potassium- 41.

Isotopes of potassium can be represented as follows:

  ${}_{19}^{39}\text{K}{,}_{19}^{40}\text{K}{,}_{19}^{41}\text{K}$

Explanation of Solution

Given information:

Potassium- 39, potassium- 40 and potassium- 41 are three isotopes of potassium.

Isotope- Isotopes are atoms of the same element having different numbers of neutrons.The mass of an atom is the mass of a single atom for a single isotope of an element. Since most of the mass of an atom is concentrated in the nucleus of an atom, the atomic mass is calculated by considering the mass of protons and mass of neutrons. Each isotope of an element has a different mass due to different numbers of neutrons. The mass of an atom is generally a whole number.

Potassium occurs in nature in three forms. These three forms are called isotopes of potassium. One isotope of potassium has a mass of 39 amu. The other two isotopes have masses of 40 amu and 41 amu respectively. Potassium- 39, potassium- 40 and potassium- 41are isotopes of potassium. All these isotopes have the same number of protons; sothe number of neutrons in potassium- 39 is one less than in potassium- 40 and two less than in potassium- 41. Similarly,Potassium- 40 has one neutron less than Potassium- 41.

Isotope symbol- Symbols for three isotopes of potassium are given below:

  ${}_{19}^{39}\text{K}{,}_{19}^{40}\text{K}{,}_{19}^{41}\text{K}$

The mass of each isotope is shown as the superscript number on top. This is a whole number calculated as the sum of the number of protons and neutrons in the atom. It is also called the mass number. The subscript number is the atomic number of the element. Here, the atomic number of potassium is 19 (from the periodic table) and the mass numbers are 39, 40 and 41 respectively. So the number of neutrons can be calculated as (39- 19), (40- 19) and (41-19) respectively.

Conclusion

The mass number of an atom is the sum of the number of protons and neutrons in an atom. Isotopes have different mass numbers but the same atomic number. ${}_{19}^{39}\text{K}{,}_{19}^{40}\text{K}{,}_{19}^{41}\text{K}$ are three isotopes of potassium.