Question

3 the element boron has two naturally occurring isotopes – one with an atomic mass of 10.01 and another with an atomic mass of 11.01. given the information provided on the periodic table, which do you think is the most abundant isotope?
a. the one with an atomic mass of 10.01.
b. the one with an atomic mass of 11.01.
c. they are both equally as abundant.
d. not enough information is provided to answer this.

Explanation:

Step1: Recall atomic mass calculation

The atomic mass of an element (on the periodic table) is a weighted average of its isotopes' masses, weighted by their relative abundances. Let the abundance of the isotope with mass \( m_1 = 10.01 \) be \( x \), and the abundance of the isotope with mass \( m_2 = 11.01 \) be \( 1 - x \) (since total abundance is 1 or 100%). The atomic mass \( M \) is given by \( M = m_1x + m_2(1 - x) \).

Step2: Check boron's actual atomic mass

From the periodic table, boron's atomic mass is approximately 10.81. Let's see the weighted average. If \( x \) is the abundance of 10.01, then \( 10.01x + 11.01(1 - x) = 10.81 \). Solving: \( 10.01x + 11.01 - 11.01x = 10.81 \) → \( -1.00x = 10.81 - 11.01 = -0.20 \) → \( x = 0.20 \)? Wait, no, wait—wait, actually, let's think about the trend. The atomic mass is closer to 11.01 than 10.01 (10.81 is 0.8 away from 10.01, 0.2 away from 11.01). Wait, no: 10.81 - 10.01 = 0.8; 11.01 - 10.81 = 0.2. So the weighted average is closer to 11.01, meaning the isotope with mass 11.01 has a higher abundance (since the average is pulled towards the more abundant isotope). Wait, wait, no—wait, my calculation was wrong. Wait, let's re-express: \( M = 10.01x + 11.01(1 - x) = 11.01 - 1.00x \). If \( M = 10.81 \), then \( 11.01 - x = 10.81 \) → \( x = 11.01 - 10.81 = 0.20 \). So the abundance of 10.01 is 20%, and 11.01 is 80%. So the isotope with mass 11.01 is more abundant. Wait, but let's confirm: the atomic mass is a weighted average. If the average is closer to a particular isotope's mass, that isotope is more abundant. Boron's atomic mass is ~10.81, which is closer to 11.01 (difference 0.2) than to 10.01 (difference 0.8). So the isotope with mass 11.01 is more abundant. So option B is correct.

Answer:

B. The one with an atomic mass of 11.01.