Question

Indium consists of two isotopes, 11349In and 11549In. If the atomic mass for indium on the periodic table is 114.8, are there more atoms of 11349In or 11549In in a sample of indium?

Accepted Answer

Step 1: Understand the problem. The atomic mass of indium on the periodic table is a weighted average of the masses of its isotopes, ¹¹³₄₉In and ¹¹⁵₄₉In. The goal is to determine which isotope is more abundant in a sample of indium based on the given atomic mass (114.8). Step 2: Recall the formula for calculating the weighted average atomic mass: $$ 	ext{Atomic Mass} = (	ext{Fraction of Isotope 1} 	imes 	ext{Mass of Isotope 1}) + (	ext{Fraction of Isotope 2} 	imes 	ext{Mass of Isotope 2}) . $$Here, the fractions represent the relative abundances of the isotopes. Step 3: Compare the given atomic mass (114.8) to the masses of the isotopes. The atomic mass is closer to 115 than to 113, which suggests that the isotope ¹¹⁵₄₉In is more abundant than ¹¹³₄₉In. Step 4: To confirm this, set up a system of equations using the weighted average formula. Let $$ x $$ represent the fraction of ¹¹³₄₉In and $$ 1 - x $$ represent the fraction of ¹¹⁵₄₉In. Substitute the values into the formula: $$ 114.8 = (x 	imes 113) + ((1 - x) 	imes 115) . $$Step 5: Solve the equation for $$ x  to $$determine the relative abundances of the isotopes. The value of $$ x $$ will indicate the fraction of ¹¹³₄₉In, and $$ 1 - x $$ will indicate the fraction of ¹¹⁵₄₉In. Based on the comparison in Step 3, expect $$ x  to be $$less than 0.5, confirming that ¹¹⁵₄₉In is more abundant.

Indium consists of two isotopes, ¹¹³₄₉In and ¹¹⁵₄₉In. If the atomic mass for indium on the periodic table is 114.8, are there more atoms of ¹¹³₄₉In or ¹¹⁵₄₉In in a sample of indium?

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Concetti chiave

Isotopes

Atomic Mass

Relative Abundance