The atomic mass of rhenium is 186.2 amu. It has two naturally occurring isotopes. Given that 37.1% of natural rhenium is rhenium–185, what is the other stable isotope?Single choice
A
190 75 Re
B
183 75 Re
C
187 75 Re
D
181 75 Re
E
189 75 Re

Question

The atomic mass of rhenium is 186.2 amu.  It has two naturally occurring isotopes. Given that 37.1% of natural rhenium is rhenium–185, what is the other stable isotope?

BlackTom AI · Accepted Answer

The problem gives the atomic mass of rhenium as 186.2 amu and that natural rhenium is 37.1% rhenium-185. The remaining 100% − 37.1% = 62.9% must be the other stable isotope.

First, convert percentages to decimals: 0.371 for Re-185 and 0.629 for the other isotope.

Use the average atomic mass formula: (fraction of isotope 1) × (mass number of isotope 1) + (fraction of isotope 2) × (mass number of isotope 2) = average atomic mass.

Plugging in the known values: 0.371 × 185 + 0.629 × (mass number of the other isotope) = 186.2.

Calculate the contribution of Re-185: 0.371 × 185 = 68.635 amu.

Subtract this from the total average mass to find the contribution needed from the other isotope: 186.2 − 68.635 = 117.565 amu.

Now solve for the mass number of the other isotope: (mass number of the other isotope) = 117.565 ÷ 0.629 ≈ 187.0.

The calculation yields a mass number very close to 187, which corresponds to the isotope listed as 187/75 Re in the options.

Evaluating the other choices quickly:
- 190/75 Re would contribute too much to the average mass given the 0.629 fraction, not matching 186.2.
- 183/75 Re would contribute too little to reach 186.2 with the 0.629 fraction.
- 181/75 Re and 189/75 Re similarly fail to reproduce the given average when weighted by 0.629 and 0.371.

Therefore, the combination that satisfies the mass balance with the given abundance is the isotope with mass number 187.

The atomic mass of rhenium is 186.2 amu. It has two naturally occurring isotopes. Given that 37.1% of natural rhenium is rhenium–185, what is the other stable isotope?Single choice

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