Chapter U1.14, Problem 4E

Interpretation Introduction

Interpretation :

Isotopes of given elements found in nature have to be determined based on the isotope graph.

Concept introduction: An atom or an element exists in many isotopic forms. Some isotopes are found naturally on Earth while some exist due to human activity. Isotopes differ in the number of neutrons. Some isotopes have stable nuclei while some have unstable nuclei.

Answer to Problem 4E

The following elements exist in nature.

${}_{12}^{24}\text{Mg}$, ${}_{35}^{81}\text{Br}$, ${}_{78}^{195}\text{Pt}$

Explanation of Solution

Given information :

Following symbols of elements are given:

${}_{12}^{24}\text{Mg}$, ${}_{35}^{81}\text{Br}$, ${}_{60}^{152}\text{Nd}$, ${}_{78}^{195}\text{Pt}$, ${}_{92}^{238}\text{U}$

Explanation :

Elements are found in one or more isotopic forms. Some isotopes have stable nuclei while some have unstable nuclei.

Stability of nucleus determines the stability of an isotope. Unstable nucleus will disintegrate. There should be a balance between the number of protons and number of neutrons to have a stable nucleus. Large atoms need more neutrons to make stable nuclei.

From the isotope graph following observations are made:

1. ${}_{12}^{24}\text{Mg}$-From the isotope graph one have to find out if there is a square that corresponds with magnesium - 24. First one has to find out how many protons and neutron this element has. It is given from the symbol that it has 12 protons. Since mass number is 24, number of neutrons is 12. There is a square on the graph that corresponds to 12 protons and 12 neutrons. Hence this isotope exists in nature.
2. ${}_{35}^{81}\text{Br}$ - From the isotope graph one have to find out if there is a square that corresponds with bromine-81. First one has to find out how many protons and neutron this element has. It is given from the symbol that it has 35 protons. Since mass number is 81, number of neutrons is 46. There is a square on the graph that corresponds to 35 protons and 86 neutrons. Hence this isotope exists in nature.
3. ${}_{60}^{152}\text{Nd}$, ${}_{78}^{195}\text{Pt}$, ${}_{92}^{238}\text{U}$
4. ${}_{60}^{152}\text{Nd}$-From the isotope graph one have to find out if there is a square that corresponds with neodymium. First one has to find out how many protons and neutron this element has. It is given from the symbol that it has 60 protons. Since mass number is 152, number of neutrons is 92. There is no square on the graph that corresponds to 60 protons and 92 neutrons. Hence this isotope does not exist in nature.
5. ${}_{78}^{195}\text{Pt}$-From the isotope graph one have to find out if there is a square that corresponds with platinum - 195. First one has to find out how many protons and neutron this element has. It is given from the symbol that it has 78 protons. Since mass number is 195, number of neutrons is 117. There is a square on the graph that corresponds to 78 protons and 117 neutrons. Hence this isotope exists in nature.
6. ${}_{92}^{238}\text{U}$ - From the isotope graph one have to find out if there is a square that corresponds with uranium - 238. First one has to find out how many protons and neutron this element has. It is given from the symbol that it has 92 protons. Since mass number is 238, number of neutrons is 146. There is no square on the graph that corresponds to 92 protons and 146 neutrons. Hence this isotope does not exist in nature.

Therefore, ${}_{12}^{24}\text{Mg}$, ${}_{35}^{81}\text{Br}$, ${}_{78}^{195}\text{Pt}$ isotopes exist in nature.

Conclusion

Each element has different number of isotopes. Some isotopes are stable while some are radioactive; some isotopes are abundantly available on earth while some are rare.