Problem 69 - Chemistry Matter and Change

Question

Xenon An isotope of xenon has an atomic number of 54 and contains 77 neutrons. What is the xenon isotope’s mass number?

Step-by-Step Solution

Answer

The mass number of the xenon isotope is 131.

Step 1: Recall the formula for calculating the mass number

The mass number (A) can be calculated using the following formula: A = atomic number (Z) + number of neutrons (N) In this case, the atomic number, Z = 54, and the number of neutrons, N = 77.

Step 2: Use the formula to calculate the mass number

Now plug the given values into the formula: A = Z + N A = 54 + 77

Step 3: Solve for the mass number

Calculate the sum of the atomic number and the number of neutrons: A = 131 The mass number of the xenon isotope is 131. So, the isotope can be represented as Xenon-131 or \(_{54}^{131}\textrm{Xe}\).

Key Concepts

Atomic Number

The atomic number, denoted as 'Z', is an essential concept in understanding elements on the Periodic Table. It is defined as the number of protons found in the nucleus of an atom. Since protons carry a positive charge, the atomic number also signifies the positive charge of the nucleus and determines the chemical properties of the atom. Every element is uniquely identified by its atomic number. For example, the element xenon (Xe) has an atomic number of 54, meaning every atom of xenon has 54 protons in its nucleus.

It's crucial to note that the atomic number is tied to an element's identity. Changing the number of protons in an atom's nucleus will change the element itself. Therefore, for the xenon isotope in our exercise, the number 54 is integral as it keeps the identity of the atom tied to xenon.

Number of Neutrons

Neutrons are subatomic particles found in the nucleus of an atom, much like protons. One of their roles is to provide stability to the nucleus by offsetting the repulsion between positively charged protons. Unlike protons, neutrons do not have an electrical charge. The number of neutrons is represented as 'N' and varies among different isotopes of the same element.

To understand any element's mass number, one must count its neutrons. The exercise given explains that a xenon isotope has 77 neutrons. While the atomic number (protons) of xenon remains constant at 54, the variation in the number of neutrons leads to different isotopes, which brings us to the next key concept.

Isotopes

Isotopes are variants of a given element that have the same number of protons (thus, the same atomic number) but a different number of neutrons. This variation in neutron number results in different mass numbers for the isotopes. For instance, while all isotopes of xenon will have 54 protons, one isotope might have 77 neutrons, and another might have, say, 75.

Isotopes are powerful in scientific research for a number of reasons. Some isotopes are stable, while others are radioactive and may decay into other elements. Understanding isotopes is not only key to chemistry and physics but also to fields like geology and medicine, where isotopes are used in dating techniques and imaging, respectively.

Xenon Isotopes

Talking specifically about xenon, this noble gas is known to have several isotopes, all with the characteristic atomic number of 54. The different isotopes of xenon have been observed with a range of neutron numbers, making the mass number of xenon isotopes vary. For example, the exercise presented refers to an isotope of xenon that has 77 neutrons, which, when combined with the 54 protons, gives a mass number of 131.

Knowing the unique mass numbers, scientists can separate isotopes of xenon (or any other element) for various applications. For instance, the isotope Xenon-131 may have different properties or uses compared to Xenon-129. Understanding the nature of xenon isotopes can lead to innovations in fields like radiation therapy, where certain isotopes are used to target and destroy cancer cells.