chem 1

Transcript fragment: Bromine isotopes

  • Bromine has two isotopes.

  • 50% has a mass of 79.

  • The transcript ends with "So we got" (incomplete); the remainder of the thought is not provided in this fragment.

Key concepts introduced in this fragment

  • Isotopes: atoms of the same element with the same number of protons but different numbers of neutrons, leading to different mass numbers.

  • Natural isotopic abundance: the fraction of each isotope found in nature. In this fragment, one isotope has an abundance of 50%.

  • Mass number: the total number of protons and neutrons in an isotope; here one isotope has mass number 79.

  • The other isotope (mass and abundance) is not stated in the fragment.

Mathematical framework for isotopic composition

  • Let there be two isotopes with masses $m1, m2$ and fractional abundances $f1, f2$.

  • The average mass (weighted by abundances) is
    ar{A} = 1 f1 m1 + f2 m2 1

  • Abundances sum to 1:
    1 f1 + f2 1 = 1

  • For two isotopes, this simplifies to
    Aˉ=f<em>1m</em>1+f<em>2m</em>2,f<em>1+f</em>2=1\bar{A} = f<em>1 m</em>1 + f<em>2 m</em>2,\quad f<em>1 + f</em>2 = 1

Worked illustration (based on the fragment)

  • Given: $f1 = 0.50$, $m1 = 79$.

  • Then
    Aˉ=0.50imes79+(1−0.50)imesm<em>2=39.5+0.50imesm</em>2\bar{A} = 0.50 imes 79 + (1 - 0.50) imes m<em>2 = 39.5 + 0.50 imes m</em>2

  • If the second isotope had mass $m2 = 81$ and abundance $f2 = 0.50$, then
    Aˉ=0.50imes79+0.50imes81=39.5+40.5=80.0\bar{A} = 0.50 imes 79 + 0.50 imes 81 = 39.5 + 40.5 = 80.0

  • Note: The above numeric example is illustrative; the actual $m_2$ is not provided in the transcript.

Significance and context

  • The average atomic mass of bromine on the periodic table is a weighted average of its isotopes' masses according to their natural abundances.

  • Understanding isotopic composition helps explain why elements have non-integer atomic masses and how measurements of isotopic ratios are used in scientific analyses.

Anticipated continuation (based on typical lecture flow)

  • The missing portion likely specifies the mass of the second bromine isotope and its abundance.

  • From there, one would compute the overall average atomic mass using the formula above.

Foundational concepts linked to this fragment

  • Isotopes vs. elements: isotopes differ in neutrons but share proton count; elements are defined by proton number.

  • Mass number vs. atomic mass unit: $m_i$ here refers to the isotope mass number; actual atomic mass on the periodic table is a weighted average in atomic mass units (amu).

  • Real-world relevance: isotopic abundances are used in chemistry, geology (isotope ratios), medicine, and environmental science.