Three isotopes of Carbon are shown above. How are these isotopes alike?

A.
They have the same number of protons and the same mass number.
B.
They have the same number of neutrons and the same mass number.
C.
They have the same number of neutrons and the same atomic number.
D.
They have the same number of protons and the same atomic number.

D. They have the same number of protons and the same atomic number.

The correct answer is D. They have the same number of protons and the same atomic number.

To determine how these isotopes are alike, we need to understand the characteristics of isotopes. Isotopes are atoms of the same element that have the same atomic number (number of protons) but different mass numbers (total number of protons and neutrons).

Let's break down the options:

A. They have the same number of protons and the same mass number.
This option suggests that all three isotopes have the same number of protons and the same mass number. However, isotopes are defined by having the same number of protons but differing in the number of neutrons, so this option is incorrect.

B. They have the same number of neutrons and the same mass number.
This option states that all three isotopes have the same number of neutrons and the same mass number. While isotopes can have different numbers of neutrons, their mass numbers can still be the same if the varying number of neutrons compensates for the difference. Therefore, this option is plausible.

C. They have the same number of neutrons and the same atomic number.
This option suggests that all three isotopes have the same number of neutrons and the same atomic number. However, isotopes are differentiated by their different numbers of neutrons, so this option is incorrect.

D. They have the same number of protons and the same atomic number.
This option states that all three isotopes have the same number of protons and the same atomic number. Since isotopes are defined by having the same number of protons, this option is correct.

Therefore, the correct answer is:

D. They have the same number of protons and the same atomic number.