Question

Given that the masses of a proton, neutron, and electron are \(1.00728,1.00867\), and \(.000549\) amu, respectively, how much missing mass is there in \({ }^{19}{ }_{9} \mathrm{~F}\) (atomic weight = \(18.9984) ?\)

Short answer

The missing mass in the \({ }^{19}{ }_{9} \mathrm{~F}\) atom is approximately 0.1588 atomic mass units (amu).

Step-by-step solution

Convert masses to atomic mass units

We are given the masses of protons, neutrons, and electrons in amu: Proton mass = 1.00728 amu Neutron mass = 1.00867 amu Electron mass = 0.000549 amu

Determine the number of protons, neutrons and electrons

For \({ }^{19}{ }_{9} \mathrm{~F}\), 9 indicates the number of protons and the number of electrons. Atomic mass number (A) is 19, and so the number of neutrons is found by subtracting the number of protons from the atomic mass number: Number of neutrons = 19 (atomic mass number) - 9 (number of protons) = 10. Therefore, we have: 9 protons 10 neutrons 9 electrons

Calculate the total mass of protons, neutrons and electrons

Total mass = (Number of protons × proton mass) + (Number of neutrons × neutron mass) + (Number of electrons × electron mass) Total mass = (9 × 1.00728) + (10 × 1.00867) + (9 × 0.000549) Total mass = 9.06552 + 10.0867 + 0.004941 Total mass = 19.157161 amu

Calculate the missing mass

Missing mass = Total mass (as calculated in step 3) - Atomic weight (given in the problem) Missing mass = 19.157161 amu - 18.9984 amu Missing mass = 0.158761 amu The missing mass in the \({ }^{19}{ }_{9} \mathrm{~F}\) atom is approximately 0.1588 atomic mass units (amu).

Key concepts

Atomic Mass Units

To understand the concept of atomic mass units (amu), let's start with the basics. An atomic mass unit is a standard unit of mass that quantifies the mass of an atom or molecule. It is used for expressing both atomic masses and molecular masses.

• 1 amu is defined as one-twelfth of the mass of a carbon-12 atom.
• This small unit helps in measuring atomic and subatomic particles with precision.

The use of amu simplifies calculations in chemistry and physics, allowing us to express very small masses in terms that are more manageable. When dealing with nuclear reactions, understanding atomic mass units is crucial as it helps in determining the stability and energy changes involved in these reactions.

Proton Mass

In any atom, the proton is a fundamental particle found in the nucleus. It has a positive charge and is crucial in defining the identity of an element. The mass of a proton is approximately 1.00728 atomic mass units (amu). This tiny particle holds a significant amount of mass relative to the entire atom.

• The mass contributes significantly to the atomic mass of an element.
• Protons, along with neutrons, make up the atomic nucleus, accounting for nearly all of an atom's mass.

The number of protons, known as the atomic number, also determines the element's chemical properties and its place in the periodic table. This is why understanding proton mass is foundational to the study of chemistry and physics.

Neutron Mass

Neutrons are uncharged particles that reside in the nucleus of an atom, right alongside protons. They play a pivotal role in adding mass without contributing to charge. A neutron has a mass of approximately 1.00867 atomic mass units (amu), slightly heavier than a proton.

• Neutrons act as a stabilizing force in the nucleus, offsetting the repulsive forces between positively charged protons.
• The number of neutrons can vary within the same element, leading to different isotopes of the element.

Understanding neutron mass is crucial when calculating the total mass of an atom and in nuclear chemistry for processes such as nuclear fission and fusion. This knowledge also helps in explaining why the mass number of isotopes can differ despite having the same chemical properties.

Electron Mass

Electrons are the lightest among the subatomic particles, carrying a negative charge and orbiting the nucleus of an atom. Although their mass is relatively negligible compared to protons and neutrons, they play a critical role in the chemistry of atoms. The mass of an electron is about 0.000549 amu.

• Due to their small mass, electrons contribute very little to the atomic mass.
• Despite their small size, electrons are crucial for chemical bond formations and reactions.

When calculating the mass of an entire atom, electron mass is usually excluded or considered negligible in certain contexts, such as nuclear binding energy calculations. Yet, the behavior and arrangement of electrons determine the chemical properties and reactivity of the element.