Log In Start studying!

Select your language

Suggested languages for you:
Answers without the blur. Sign up and see all textbooks for free! Illustration


Fundamentals Of Physics
Found in: Page 1303

Answers without the blur.

Just sign up for free and you're in.


Short Answer

A periodic table might list the average atomic mass of magnesium as being 24.312u, which the result of weighting the atomic masses of the magnesium isotopes is according to their natural abundances on Earth. The three isotopes and their masses are 24Mg(23.98504u), 25Mg(23.98584u) , and 26Mg(23.9859u). The natural abundance of 24Mg is 78.99% by mass (that is, 78.99% of the mass of a naturally occurring sample of magnesium is due to the presence of24Mg).What is the abundance of (a) 25Mg and (b) 26Mg?

  1. The abundance of M25g is 9.303%.
  2. The abundance of M26g is 11.71%.
See the step by step solution

Step by Step Solution

Step 1: Write the given data

  1. Average atomic mass of magnesium, Mmg=24.312u
  2. The mass of the isotope 24Mg, M1=23.98504u
  3. The mass of the isotope 25Mg, M2=24.98584u
  4. The mass of the isotope 26Mg, M3=24.98259u
  5. The natural abundance of the isotope 24Mg is 78.99% of its mass.

Step 2: Understanding the concept of natural abundance  

The abundance of the three isotopes represents their percent of mass percent in the environment. Considering that there are three isotopes of magnesium, we can get an equation of the total abundance of the three isotopes to be 100% of the natural magnesium substance. Thus, using this concept, we can calculate the abundance of the two other isotopes that are unknown.

Step 3: a) Calculate the abundance of isotope 25Mg

Let f24 be the abundance of 24Mg, let f25 be the abundance of 25Mg, and let f26 be the abundance of 26Mg. Then, the entry in the periodic table for Mg is:

24.312=23.98504f24+24.98584f25+25.98259f26 ….. (a)

Since, there are only three isotopes f24+f25+f26=1. Solving for f25 and f26, we have the above equation as follows:

f26=1-f24-f25 …… (b)

Now, substituting this above value and f24=0.7899 in equation (a), determine the abundance of isotope Mg25 as follows:

role="math" localid="1661585620014" 24.312=23.985040.7899+24.98259-24.982590.7899-25.98259f25f25=0.09303f25=9.303%

Hence, the value of abundance is 9.303%.

Step 4: b) Calculate the abundance of isotope 26Mg

Now, substitute the values f24=0.7899 and role="math" localid="1661585674376" f25=0.09303 in equation (b), solve to obtain the abundance of isotope M26g as follows:

f26=1-0.7899-0.09303 =0.1171 =11.71%

Hence, the value of abundance is 11.71%.


Want to see more solutions like these?

Sign up for free to discover our expert answers
Get Started - It’s free

Recommended explanations on Physics Textbooks

94% of StudySmarter users get better grades.

Sign up for free
94% of StudySmarter users get better grades.