Question

Suppose that carbon-12 was assigned a mass of exactly 20 amu instead of 12 amu. What is the average atomic mass of hydrogen, argon, potassium, and mercury based on this standard?

Answer 1

If carbon-12 was assigned a mass of exactly 20 amu instead of 12 amu, we need to adjust the atomic masses of other elements accordingly.

The average atomic mass of an element is determined by considering the relative abundance of its isotopes and their respective masses. Since hydrogen, argon, potassium, and mercury have multiple isotopes, we need to take their isotopic abundances into account.

Here are the adjusted average atomic masses of the given elements based on the hypothetical scenario:

1. Hydrogen (H):

   • Hydrogen-1 (protium) has an atomic mass of approximately 1.0078 amu.
   • Hydrogen-2 (deuterium) has an atomic mass of approximately 2.0141 amu.
   • Hydrogen-3 (tritium) has an atomic mass of approximately 3.0160 amu.

   To calculate the average atomic mass of hydrogen, we consider the relative abundances of these isotopes. Since hydrogen-2 and hydrogen-3 are present in extremely small quantities, their contribution to the average atomic mass is negligible. Therefore, the average atomic mass of hydrogen in this scenario is approximately 1.0078 amu.

2. Argon (Ar):

   • Argon-36 has an atomic mass of approximately 35.9675 amu.
   • Argon-38 has an atomic mass of approximately 37.9627 amu.
   • Argon-40 has an atomic mass of approximately 39.9624 amu.

   To calculate the average atomic mass of argon, we consider the relative abundances of these isotopes. The most abundant isotope is argon-40, which occurs at a relative abundance of about 99.6%. The contribution from the other isotopes is minimal. Therefore, the average atomic mass of argon in this scenario is approximately 39.9624 amu.

3. Potassium (K):

   • Potassium-39 has an atomic mass of approximately 38.9637 amu.
   • Potassium-40 has an atomic mass of approximately 39.9637 amu.
   • Potassium-41 has an atomic mass of approximately 40.9618 amu.

   To calculate the average atomic mass of potassium, we consider the relative abundances of these isotopes. The most abundant isotope is potassium-39, which occurs at a relative abundance of about 93.3%. The contributions from the other isotopes are smaller but still significant. Therefore, the average atomic mass of potassium in this scenario is approximately 39.9637 amu.

4. Mercury (Hg):

   • Mercury-196 has an atomic mass of approximately 195.9658 amu.
   • Mercury-198 has an atomic mass of approximately 197.9668 amu.
   • Mercury-199 has an atomic mass of approximately 198.9683 amu.
   • Mercury-200 has an atomic mass of approximately 199.9683 amu.
   • Mercury-201 has an atomic mass of approximately 200.9703 amu.
   • Mercury-202 has an atomic mass of approximately 201.9706 amu.
   • Mercury-204 has an atomic mass of approximately 203.9735 amu.

   To calculate the average atomic mass of mercury, we consider the relative abundances of these isotopes. The most abundant isotope is mercury-202, which occurs at a relative abundance of about 29.8%. The contributions from the other isotopes are smaller but still significant. Therefore, the average atomic mass of mercury in this scenario is approximately 201.9706 amu.

Please note that these values are hypothetical and are provided based on the given scenario. In reality, carbon-12 is assigned a mass of exactly 12 amu, and the average atomic masses of elements are determined based on the actual isotopic abundances and atomic masses.