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Chapter 4: Problem 62

What do the superscript and subscript in the notation \(_{19}^{40} \mathrm{K}\) represent?

Short Answer

Expert verified
In the notation \(_{19}^{40} \mathrm{K}\), the subscript "19" represents the atomic number (number of protons) of the chemical element Potassium, and the superscript "40" represents the mass number (sum of protons and neutrons) of the specific isotope of Potassium. Therefore, this isotope has 19 protons and \(40 - 19 = 21\) neutrons in its nucleus.

Step by step solution

01

Identifying the Element

The notation given is \(_{19}^{40} \mathrm{K}\). Here, "K" represents the chemical element, which in this case is Potassium.
02

Understanding the Subscript

The subscript, denoted by the number 19 in the notation \(_{19}^{40} \mathrm{K}\), represents the atomic number of the chemical element. The atomic number tells us the number of protons in the nucleus of an atom of the element. In this case, the atomic number of Potassium is 19, which means it has 19 protons in its nucleus.
03

Understanding the Superscript

The superscript, denoted by the number 40 in the notation \(_{19}^{40} \mathrm{K}\), represents the mass number of the specific isotope of the chemical element. The mass number is the sum of the number of protons and neutrons in the nucleus of an atom. In this case, the mass number of this Potassium isotope is 40, which means it has a total of 40 protons and neutrons in its nucleus.
04

Calculating the Number of Neutrons

We can calculate the number of neutrons in the nucleus of this specific isotope by subtracting the atomic number (number of protons) from the mass number. Number of neutrons = Mass number - Atomic number Number of neutrons = 40 - 19 Number of neutrons = 21 So, this particular isotope of Potassium, denoted by \(_{19}^{40} \mathrm{K}\), has 19 protons and 21 neutrons in its nucleus.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Atomic Number
Understanding the atomic number is crucial for anyone delving into chemistry. This fundamental concept refers to the number of protons present in the nucleus of an atom, and it is the identity card for an element. Each element has a unique atomic number, making it distinguishable from others. For example, when we see the subscript in the chemical notation \(_{19}^{40}\mathrm{K}\), that subscript, 19 in this case, tells us exactly how many protons are in the nucleus of a potassium atom. Since all atoms of an element have the same number of protons, the atomic number for any given element is always consistent, no matter what isotope of the element you're dealing with.

  • The atomic number defines the element.
  • It determines the element's position on the periodic table.
  • It also helps in predicting chemical behavior.
Mass Number
Alongside the atomic number, the mass number provides essential information about an atom's nucleus. It is represented as the superscript in chemical notation, such as the number 40 in \(_{19}^{40}\mathrm{K}\). The mass number is the total count of protons and neutrons in an atom's nucleus, two types of particles collectively known as nucleons. Because electrons have negligible mass, the mass number essentially tells us the atom's approximate atomic mass. Here's an easy way to remember this:

  • Protons and neutrons have a unitary, albeit slightly different, mass.
  • The atomic mass is roughly equivalent to the mass number.
  • Different isotopes of an element have different mass numbers due to varying numbers of neutrons.
Isotopes
Isotopes are 'siblings' of chemical elements, identical in the number of protons but differing in the number of neutrons. Returning to our example of \(_{19}^{40}\mathrm{K}\), while all potassium atoms have 19 protons (atomic number 19), this particular isotope has a mass number of 40. Why is this important? Isotopes have nearly identical chemical properties but may have very different physical properties, such as stability and radioactivity. Some isotopes are stable, while others are radioactive and decay over time, a trait utilized in carbon dating and medical diagnoses.

  • Isotopes share the same atomic number but have different mass numbers.
  • They can be stable or radioactive.
  • Isotopic variations are vital in scientific research and medical applications.
Protons and Neutrons
These subatomic particles are building blocks of atoms and play a critical role in defining an atom's characteristics. Protons, found in the nucleus, have a positive charge and determine the atomic number and, thus, the element's identity. Neutrons also reside in the nucleus and possess no electric charge. Their primary role is to add mass to the atom and stabilize the nucleus, which prevents the protons from repelling one another due to their like charges. The balance between protons and neutrons is a delicate one, and variations in neutron numbers can lead to the creation of various isotopes of an element.

  • Protons define the element's identity and its chemical properties.
  • Neutrons contribute to atomic stability and can cause the existence of isotopes.
  • The number of these particles affects the atom's atomic number and mass number.

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