A Robot Spacecraft Returned Samples from the Planetesimal 98765 ALEKS: Complete Guide & Step-by-Step Solutions
If you are working through ALEKS chemistry and have encountered the problem that begins with “A robot spacecraft returned samples from the planetesimal 98765 ALEKS, located in the outer Solar System”, you are in the right place.
This is one of the most widely searched ALEKS chemistry problems because it appears across General Chemistry I courses in hundreds of universities, and it comes in several variations — different elements, different isotopes, different abundance percentages. Students who understand the core concept can solve every version of this problem in under two minutes. Students who don’t understand the concept keep searching for the specific numbers that match their version.
This guide teaches you both: the step-by-step method for solving any version of this problem, worked examples for the most common element variations (molybdenum, ruthenium, tin), and a clear conceptual explanation of what the question is actually testing. By the end, you will not need to search for this problem again.
What Is the Planetesimal 98765 ALEKS Problem?
The full problem reads something like this:
“A robot spacecraft returned samples from the planetesimal 98765 ALEKS, located in the outer Solar System. Mass-spectroscopic analysis produced the following data on the isotopes of [element] in these samples. Use these measurements to complete the entry for [element] in the Periodic Table that would be used on 98765 ALEKS. Be sure your answers have the correct number of significant digits. Caution: your correct answer will have the same format but not necessarily the same numbers as the entry for [element] in the Periodic Table we use here on Earth.”
The element changes depending on which version of ALEKS you have. Common versions use molybdenum (Mo), ruthenium (Ru), and tin (Sn), but the method is exactly the same regardless of which element appears in your version.
What is Planetesimal 98765 ALEKS?
A planetesimal is a small solid body found in the outer Solar System — typically a rocky or icy object left over from the formation of planets. Planetesimal 98765 ALEKS is a fictional object created specifically for this ALEKS chemistry problem. It is a hypothetical Kuiper Belt object used as a creative scenario for a straightforward chemistry calculation. The “ALEKS” in the name refers directly to the homework platform itself. There is no real astronomical object with this designation.
The fictional framing is intentional: by saying the spacecraft collected samples from another world, the question forces you to calculate atomic mass only from the isotopic data provided — you cannot simply look up the element’s atomic mass on a standard Periodic Table, because on “98765 ALEKS” only those two isotopes exist.
What Chemistry Concept Is Being Tested?
This problem tests your ability to calculate average atomic mass (also called atomic weight) from isotopic abundance data.
On Earth, every element exists as a mixture of naturally occurring isotopes in specific proportions. The atomic mass shown on the Periodic Table is a weighted average of all those isotopes based on their natural abundances on Earth. On planetesimal 98765 ALEKS, the isotopic mix is different — so the atomic mass entry for the Periodic Table on that world would be different from ours.
Your job is to calculate what that atomic mass would be, using only the data provided.
The Formula: How to Calculate Average Atomic Mass
The formula for average atomic mass is:
Average Atomic Mass = (Mass of Isotope 1 × Relative Abundance 1) + (Mass of Isotope 2 × Relative Abundance 2)
Important rules before you calculate:
Convert percentages to decimals. If the abundance is given as 42%, you use 0.42 in the formula. If it is given as 58%, you use 0.58.
The abundances must add up to 1.00 (or 100%). If your two isotopes account for 42% and 58%, that adds to 100% — good. If they don’t add to 100%, re-read the problem.
Significant figures matter. ALEKS is strict about this. The final answer should be rounded to the number of significant digits indicated in the problem — usually 2 or 3.
The atomic number never changes. Regardless of which planet or planetesimal the sample comes from, the atomic number (number of protons) for an element is always the same. Only the atomic mass changes based on isotopic abundances. This is a key conceptual point the problem is testing.
Worked Example 1: Molybdenum (Mo)
The Problem:
A robot spacecraft returned samples from the planetesimal 98765 ALEKS. Mass-spectroscopic analysis produced the following data on the isotopes of molybdenum:
| Isotope | Mass (amu) | Relative Abundance |
|---|---|---|
| ⁹⁶Mo | 95.90 | 42% |
| ⁹⁷Mo | 96.91 | 58% |
Use these measurements to complete the entry for molybdenum in the Periodic Table that would be used on 98765 ALEKS. Round your entry for atomic mass to 2 significant digits.
Step 1: Convert percentages to decimals
42% becomes 0.42 58% becomes 0.58
Check: 0.42 + 0.58 = 1.00 ✓
Step 2: Multiply each isotope mass by its abundance
⁹⁶Mo: 95.90 × 0.42 = 40.278 ⁹⁷Mo: 96.91 × 0.58 = 56.2078
Step 3: Add the results
40.278 + 56.2078 = 96.4858
Step 4: Round to the required significant digits
Rounded to 2 significant digits: 96 amu
The Periodic Table entry for Mo on 98765 ALEKS: Atomic number: 42 (this never changes) Symbol: Mo Atomic mass: 96 amu
Why is this different from Earth’s Periodic Table? On Earth, molybdenum has seven naturally occurring isotopes with abundances spread across a wider range, giving it an atomic mass of approximately 95.96 amu. On 98765 ALEKS, only these two isotopes exist in these specific proportions, producing a slightly different weighted average.
Worked Example 2: Ruthenium (Ru)
The Problem:
A robot spacecraft returned samples from the planetesimal 98765 ALEKS. Mass-spectroscopic analysis produced the following data on the isotopes of ruthenium:
| Isotope | Mass (amu) | Relative Abundance |
|---|---|---|
| ¹⁰¹Ru | 100.905 | 37.7% |
| ¹⁰³Ru | 102.905 | 62.3% |
Use these measurements to complete the entry for ruthenium in the Periodic Table that would be used on 98765 ALEKS.
Step 1: Convert percentages to decimals
37.7% becomes 0.377 62.3% becomes 0.623
Check: 0.377 + 0.623 = 1.000 ✓
Step 2: Multiply each isotope mass by its abundance
¹⁰¹Ru: 100.905 × 0.377 = 38.04119 ¹⁰³Ru: 102.905 × 0.623 = 64.11082
Step 3: Add the results
38.04119 + 64.11082 = 102.152
Step 4: Round appropriately
Rounded to 3 significant digits: 102 amu
The Periodic Table entry for Ru on 98765 ALEKS: Atomic number: 44 Symbol: Ru Atomic mass: 102 amu
Worked Example 3: Tin (Sn)
The Problem:
A robot spacecraft returned samples from the planetesimal 98765 ALEKS. Mass-spectroscopic analysis produced the following data on the isotopes of tin:
| Isotope | Mass (amu) | Relative Abundance |
|---|---|---|
| ¹¹⁵Sn | 114.90 | 91.5% |
| ¹¹⁷Sn | 116.90 | 8.5% |
Use these measurements to complete the entry for tin in the Periodic Table that would be used on 98765 ALEKS.
Step 1: Convert percentages to decimals
91.5% becomes 0.915 8.5% becomes 0.085
Check: 0.915 + 0.085 = 1.000 ✓
Step 2: Multiply each isotope mass by its abundance
¹¹⁵Sn: 114.90 × 0.915 = 105.1335 ¹¹⁷Sn: 116.90 × 0.085 = 9.9365
Step 3: Add the results
105.1335 + 9.9365 = 115.07
Step 4: Round appropriately
Rounded to 3 significant digits: 115 amu
The Periodic Table entry for Sn on 98765 ALEKS: Atomic number: 50 Symbol: Sn Atomic mass: 115 amu
How to Solve Any Version of This Problem
ALEKS randomizes the numbers in this problem, so your isotope masses and abundances may be slightly different from the examples above. The element may also be different. Regardless of the specific numbers, the method is always identical.
The universal approach:
First, identify the two isotopes, their masses in amu, and their relative abundances as percentages. Second, convert both percentages to decimals by dividing by 100. Third, multiply each isotope mass by its decimal abundance. Fourth, add the two products together. Fifth, round your answer to the number of significant digits the problem specifies.
The atomic number in the Periodic Table entry is always the standard atomic number for that element — it does not change based on the sample source.
Key Concepts This Problem Tests
What are isotopes?
Isotopes are atoms of the same element that have the same number of protons (same atomic number) but different numbers of neutrons, giving them different mass numbers. For example, ⁹⁶Mo and ⁹⁷Mo are both molybdenum — both have 42 protons — but ⁹⁶Mo has 54 neutrons while ⁹⁷Mo has 55 neutrons.
What is atomic mass?
Atomic mass (also called atomic weight) is the weighted average mass of all naturally occurring isotopes of an element, taking into account how abundant each isotope is. It is measured in atomic mass units (amu). Because it is a weighted average, it is almost never a whole number.
What is mass-spectroscopic analysis?
Mass spectrometry is an analytical technique that separates atoms or molecules by their mass-to-charge ratio, allowing scientists to identify which isotopes of an element are present in a sample and in what proportions. In the fictional scenario of the 98765 ALEKS problem, the robot spacecraft uses this technique to analyze the elemental composition of material collected from the planetesimal’s surface.
Why does isotopic abundance vary between worlds?
On Earth, the isotopic abundances of elements were set during the formation of the Solar System and have remained largely stable due to the specific nuclear processes involved in Earth’s history. On a different Solar System body — especially an outer Solar System planetesimal that formed under different conditions and experienced different exposure to cosmic radiation — the proportions of isotopes could theoretically be different. This is the scientific premise that makes the ALEKS problem plausible.
Why does the atomic number never change?
The atomic number is defined by the number of protons in the nucleus. An atom of molybdenum always has 42 protons — if it had a different number of protons, it would be a different element entirely. The number of neutrons can vary (producing different isotopes), but the number of protons is fixed by the identity of the element. This is why the Periodic Table entry for Mo on planetesimal 98765 ALEKS still shows atomic number 42, even though the atomic mass is different from the terrestrial value.
Common Mistakes to Avoid
Forgetting to convert percentages to decimals. This is the most common error. If you multiply 95.90 × 42 instead of 95.90 × 0.42, your answer will be 100 times too large. Always divide by 100 first.
Using the wrong atomic number. Some students try to change the atomic number based on the fictional scenario. The atomic number is an intrinsic property of the element — it cannot change without the atom becoming a different element entirely.
Rounding too early. Carry at least four decimal places through your intermediate calculations, then round only the final answer to the required significant figures. Rounding at each step introduces cumulative error.
Confusing mass number with atomic mass. The mass number (e.g., 96 in ⁹⁶Mo) is a whole number representing the total count of protons and neutrons in a specific isotope. The atomic mass is the precise measurement in amu, which may include decimal values (e.g., 95.90 amu). Use the precise amu values given in the table, not the superscript mass numbers, in your calculation.
Not checking that abundances sum to 100%. If the two abundances in the problem do not add to 100%, either there is a typo in the problem or you are misreading the table. A weighted average only works correctly when the weights sum to 1.00.
Practice Problems
Use the method described above to solve these practice versions before checking the answers.
Practice Problem 1
Isotope data from planetesimal 98765 ALEKS for an unknown element X:
| Isotope | Mass (amu) | Relative Abundance |
|---|---|---|
| X-63 | 62.93 | 69.2% |
| X-65 | 64.93 | 30.8% |
Calculate the average atomic mass of element X on 98765 ALEKS.
Answer: (62.93 × 0.692) + (64.93 × 0.308) = 43.5476 + 19.9984 = 63.55 amu
(This is copper, Cu — and notably very close to its Earth value of 63.55 amu, because the isotopic abundances used match Earth’s natural abundances closely.)
Practice Problem 2
Isotope data for element Y:
| Isotope | Mass (amu) | Relative Abundance |
|---|---|---|
| Y-107 | 106.905 | 55.0% |
| Y-109 | 108.905 | 45.0% |
Answer: (106.905 × 0.55) + (108.905 × 0.45) = 58.798 + 49.007 = 107.80 amu
(This is silver, Ag — again matching Earth values closely when the same abundances are used.)
Frequently Asked Questions
What is the planetesimal 98765 ALEKS?
Planetesimal 98765 ALEKS is a fictional outer Solar System body created by the ALEKS homework platform as the setting for a chemistry problem about isotopic abundance and average atomic mass calculation. It is not a real astronomical object. The name includes “ALEKS” as a direct reference to the platform that uses this scenario.
Why does this problem say “the Periodic Table that would be used on 98765 ALEKS”?
The problem is forcing you to calculate atomic mass from scratch using only the isotopic data provided, rather than simply looking up the element’s atomic mass on Earth’s Periodic Table. On a different world where the same element exists with a different isotopic mix, the weighted average atomic mass would be different — so the Periodic Table entry would show a different value.
Does the atomic number change in this problem?
No. The atomic number is the number of protons in the nucleus and defines the identity of the element. It is always the same for a given element regardless of where in the universe the sample comes from. Only the atomic mass (weighted average of isotopes) changes based on isotopic abundances.
How do I know how many significant figures to use?
The problem usually specifies directly — “round your entry for atomic mass to 2 significant digits” or “3 significant digits.” If it says to be sure your answers have the correct number of significant digits without specifying, match the number of significant figures to those given in the data (the masses and abundances provided in the table).
What elements does this problem appear with?
The most commonly reported versions use molybdenum (Mo), ruthenium (Ru), and tin (Sn). However, ALEKS uses a large bank of variations and the element in your version may be different. The calculation method is identical regardless of which element appears.
Is this a real chemistry concept or just a made-up problem?
The chemistry concept is completely real. Average atomic mass calculation from isotopic abundance data is a core General Chemistry topic. The fictional spacecraft and planetesimal are just creative framing to make the problem more engaging and to prevent students from simply looking up the answer.
What is mass-spectroscopic analysis?
Mass spectrometry is a real and widely used analytical technique that measures the mass-to-charge ratio of ions to identify the isotopic composition of a sample. In the ALEKS scenario, the robot spacecraft uses this method to analyze the elemental composition of material collected from the planetesimal’s surface — a plausible application of real technology.
Conclusion
The “a robot spacecraft returned samples from the planetesimal 98765 ALEKS” problem is, at its core, a straightforward weighted average calculation. The fictional scenario is creative and memorable, but the math underneath it is the same calculation you will perform dozens of times in a General Chemistry course.
Master the four-step method — identify isotopes and abundances, convert percentages to decimals, multiply and sum, round correctly — and you can solve every version of this problem that ALEKS generates, regardless of which element, which isotope masses, or which abundance percentages appear in your specific assignment.
Understanding why the atomic number stays fixed while the atomic mass changes is the deeper conceptual insight the problem is testing. That understanding connects this problem to everything else you will learn about atomic structure, the Periodic Table, and why isotopes matter in chemistry and beyond.