Question

Strontium has four isotopes with the following masses: \(83.9134\) amu \((0.56 \%), 85.9094 \mathrm{amu}(9.86 \%), 86.9089 \mathrm{amu}(7.00 \%)\), and \(87.9056(82.58 \%)\) Calculate the atomic mass of strontium.

Short answer

Question: Calculate the atomic mass of strontium, given the mass and percentage abundance of its isotopes: 83.9134 amu (0.56%), 85.9094 amu (9.86%), 86.9089 amu (7.00%), and 87.9056 amu (82.58%). Answer: The atomic mass of strontium is approximately 87.60 amu.

Step-by-step solution

Convert percentage abundance into decimal values

To convert percentage abundance into decimal values, divide the percentage by 100. For Strontium: - Isotope 1: 0.56 / 100 = 0.0056 - Isotope 2: 9.86 / 100 = 0.0986 - Isotope 3: 7.00 / 100 = 0.0700 - Isotope 4: 82.58 / 100 = 0.8258

Multiply the mass of each isotope by their respective decimal abundances

Now that we have the decimal value for each isotope's abundance, multiply it with the respective mass of the isotope. For Strontium: - Isotope 1: 0.0056 × 83.9134 = 0.46991 - Isotope 2: 0.0986 × 85.9094 = 8.46766 - Isotope 3: 0.0700 × 86.9089 = 6.08362 - Isotope 4: 0.8258 × 87.9056 = 72.58377

Calculate the atomic mass of strontium

The atomic mass of strontium is the sum of the multiplied values obtained in step 2: Atomic Mass = 0.46991 + 8.46766 + 6.08362 + 72.58377 = 87.60496 Thus, the atomic mass of strontium is approximately 87.60 amu.

Key concepts

Isotopic Abundance

Understanding isotopic abundance is crucial for calculating the atomic mass of an element like strontium. Isotopes are atoms of the same element that have the same number of protons but differing numbers of neutrons, giving them different atomic masses. Isotopic abundance refers to the percentage of each isotope present in a naturally occurring sample of an element.

For instance, if a sample contains two isotopes of element X, one might find that isotope X-1 comprises 70% of the sample while isotope X-2 makes up 30%. These percentages are the isotopic abundances, which tell us how much of each isotope we would expect to find in nature. These values are essential because the atomic mass of an element is the weighted average of the masses of its isotopes, based on their natural abundances.

To illustrate further, in a hypothetical scenario where isotope X-1 has a mass of 10 amu and X-2 has a mass of 20 amu, you wouldn’t simply take the average of 10 and 20 to find the atomic mass. Instead, you’d use their isotopic abundances to calculate a weighted average, which would be closer to 13 amu if we weigh the mass by their natural abundances (70% of 10 amu plus 30% of 20 amu).

Atomic Mass Unit (amu)

An atomic mass unit, abbreviated as amu, is a unit of mass used to express atomic and molecular weights. It is defined as one twelfth of the mass of an unbound neutral atom of carbon-12 at rest and in its ground state. One amu is equivalent to approximately 1.66053906660 × 10^-24 grams.

This standard unit allows chemists and physicists to compare the masses of different atoms on a scale that makes sense, given the extremely small mass of individual atoms. When calculating the atomic mass of an element, such as strontium, the masses of its isotopes are usually given in amu. These values are then combined with the isotopic abundances to find the average atomic mass of the element, which is what one would generally find on the periodic table.

Strontium Isotopes

Strontium is an alkaline earth metal with atomic number 38, indicating that it has 38 protons in its nucleus. It has several naturally occurring isotopes, each with a different number of neutrons and therefore a different atomic mass. Analyzing the strontium isotopes is important for various applications, including geological dating and medical treatments.

In the given problem, we are provided with the masses and abundances of four isotopes of strontium. Scientists have determined these values through meticulous experimentation and observation. Knowing the exact mass and relative abundance of each isotope allows us to calculate the average atomic mass of strontium, which is the weighted sum of the masses of each isotope, taking their relative abundances into account.

Percentage Abundance to Decimal

When calculating atomic mass, converting the percentage abundances of isotopes to decimal form is a fundamental step. This process is straightforward: you simply divide the given percentage by 100. The reason this step is necessary is because the percentage form isn't compatible with mathematical operations needed to calculate the weighted average; we need a pure number without the percentage sign.

For example, if an isotope has an abundance of 50%, we convert this to 0.50 in decimal form. This means that for every hundred atoms of this element, 50 of them would be this specific isotope. This conversion allows us to properly calculate the weighted average by multiplying the mass of each isotope by its respective decimal abundance value, which is essentially its fractional representation.