Question

A scientist in the distant future has traveled to the Earth-like planet Kepler-186 in the Cygnus Constellation to determine if the planet can support human life. While on the planet, the scientist discovers a new element, which is given the atomic symbol, Aj. Upon careful analysis of Aj, the scientist gathers the following isotope data:

Aj-315 - Atomic Mass: 315.0000312 amu, Abundance: 75.219%

Aj-316 - Atomic Mass: 316.0029841 amu, Abundance: 0.0493%

Aj-317 - Atomic Mass: 317.0004313 amu, Abundance: 24.723%

What is the average atomic mass of this new element Aj?

Answer 1

Average atomic mass

Where, M represents the atomic mass of the isotopes in amu and A represents their abundance in percent.

For 3 isotopes with M₁, M₂, M₃ atomic masses and with respective abundances A₁ %, A₂ %, A₃ % then the above formula can be written as

Average atomic mass

Here,

M₁ = 315.0000312 amu with A₁ = 75.219 %

M₂ = 316.0029841 amu with A₂ = 0.0493 %

M₂ = 317.0004313 amu with A₃ = 24.723 %

Thus, the average atomic mass

Therefore, the average atomic mass of the new element Aj = 315.4676796 amu