Which of the following statements about isotopes is/are true?

a. Because isotopes have different numbers of neutrons, they have different mass numbers.
b. because neutrons determine an atom's chemical properties, isotopes of the same element are very different.
C. isotopes are atoms with the same number of protons but different numbers of neutrons.
d. isotopes have different atomic numbers because they have different numbers of protons.
e. Isotopes are chemically alike because they ahve the same number of protons and electrons.

The correct statement about isotopes is:

c. isotopes are atoms with the same number of protons but different numbers of neutrons.

Explanation: Isotopes are variants of a particular chemical element that have the same number of protons in their atomic nucleus but differ in the number of neutrons. This difference in the number of neutrons results in isotopes having different mass numbers. The number of neutrons in an atom does not significantly affect its chemical properties, so isotopes of the same element are chemically similar. Isotopes do not have different atomic numbers or different numbers of protons.

The correct statement(s) about isotopes are:

a. Because isotopes have different numbers of neutrons, they have different mass numbers.
c. Isotopes are atoms with the same number of protons but different numbers of neutrons.

To understand why these statements are true, let's break them down:

a. Because isotopes have different numbers of neutrons, they have different mass numbers.
Isotopes of an element are atoms that have the same number of protons (which determines the element) but different numbers of neutrons. Since neutrons contribute to the mass of an atom, isotopes of the same element have different mass numbers. For example, hydrogen has three isotopes: hydrogen-1 (1 proton, 0 neutrons), hydrogen-2 or deuterium (1 proton, 1 neutron), and hydrogen-3 or tritium (1 proton, 2 neutrons). Each of these isotopes has a different mass number.

c. Isotopes are atoms with the same number of protons but different numbers of neutrons.
This statement is correct. Isotopes have the same number of protons, which is what defines the element. However, they have different numbers of neutrons, leading to differences in their mass numbers. The different number of neutrons does not significantly affect the chemical properties of an atom, as those properties are mainly determined by the number and arrangement of electrons.

b. because neutrons determine an atom's chemical properties, isotopes of the same element are very different.
This statement is incorrect. Neutrons do not determine an atom's chemical properties. Chemical properties are primarily determined by the arrangement and behavior of electrons, specifically the number of valence electrons and how they interact with other atoms. Isotopes of the same element have the same number of protons (and therefore the same electron configuration) and similar chemical properties.

d. isotopes have different atomic numbers because they have different numbers of protons.
This statement is incorrect. Atomic number refers to the number of protons in an atom, which does not change for isotopes of the same element. It is the number of protons that determines the identity of the element.

e. Isotopes are chemically alike because they have the same number of protons and electrons.
This statement is partly correct. Isotopes have the same number of protons and electrons, which means they have the same overall charge and similar chemical behavior. However, isotopes may have different mass numbers due to their different numbers of neutrons. This difference in mass may result in slight variations in physical properties, such as density or boiling point, but not in their chemical properties.

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A, C, E.