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Chapter 2: Problem 10

Consider two isotopes Fe-54 and Fe-56. (a) Write the nuclear symbol for both isotopes. (b) How do they differ from each other?

Short Answer

Expert verified
The nuclear symbols for the isotopes are: - Fe-54: $^{54}_{26}\textrm{Fe}$ - Fe-56: $^{56}_{26}\textrm{Fe}$ The main difference between these two isotopes is the number of neutrons in their nucleus. Fe-54 has 28 neutrons, while Fe-56 has 30 neutrons.

Step by step solution

01

(a) Nuclear Symbol for Isotopes Fe-54 and Fe-56

Isotopes are atoms of the same element but have different numbers of neutrons. They have the same atomic number (Z) but different mass numbers (A). To write the nuclear symbol for isotopes, we use the following format: $$ ^{A}_{Z}\textrm{X} $$ Where A is the mass number, Z is the atomic number, and X is the element symbol. For iron (Fe), its atomic number (Z) is 26. The given isotopes are Fe-54 and Fe-56, which means their mass numbers (A) are 54 and 56, respectively. Using the format mentioned above, the nuclear symbols for the isotopes are: $$ ^{54}_{26}\textrm{Fe},\ ^{56}_{26}\textrm{Fe} $$
02

(b) Differences between Fe-54 and Fe-56

Both Fe-54 and Fe-56 isotopes have the same atomic number (26), which means they have the same number of protons and electrons. The difference between these isotopes lies in their mass number (A), which represents the total number of protons and neutrons in the nucleus. Fe-54 has a mass number of 54, while Fe-56 has a mass number of 56. Subtracting the atomic number (26) from the mass numbers, we can determine the number of neutrons for each isotope: - $$\textrm{Neutrons in Fe-54} = 54 - 26 = 28$$ - $$\textrm{Neutrons in Fe-56} = 56 - 26 = 30$$ Therefore, the difference between the two isotopes is the number of neutrons. Fe-54 has 28 neutrons, while Fe-56 has 30 neutrons.

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