Question

Determine the number of protons and neutrons in each isotope of chromium and use the listed natural abundances and masses to calculate its atomic mass. \(\begin{array}{ccc}\text { Cr-50 } & 4.345 \% & 49.9460 \mathrm{amu} \\ \text { Cr-52 } & 83.79 \% & 51.9405 \mathrm{amu} \\ \text { Cr-53 } & 9.50 \% & 52.9407 \mathrm{amu} \\ \text { Cr-54 } & 2.365 \% & 53.9389 \mathrm{amu}\end{array}\)

Short answer

Chromium has 24 protons. It has 26, 28, 29, and 30 neutrons in isotopes Cr-50, Cr-52, Cr-53, and Cr-54 respectively. The atomic mass of chromium is approximately 51.9961 amu.

Step-by-step solution

- Determine Number of Protons

The number of protons in an element is equal to its atomic number. For chromium (Cr), the atomic number is 24, which means each isotope has 24 protons.

- Determine Number of Neutrons in Each Isotope

The number of neutrons in an isotope is equal to the mass number of the isotope minus the number of protons. For Cr-50, Cr-52, Cr-53, and Cr-54, the number of neutrons is 50 - 24, 52 - 24, 53 - 24, and 54 - 24, respectively.

- Calculating Weighted Average Atomic Mass

To find the atomic mass of chromium, multiply the mass of each isotope by its natural abundance and sum the products. The natural abundance must be converted to decimal form by dividing by 100. Atomic mass = (0.04345*49.9460) + (0.8379*51.9405) + (0.0950*52.9407) + (0.02365*53.9389).

- Complete the Calculation

Now add the values calculated in the previous step to find the weighted average atomic mass of chromium.

Key concepts

Isotopes of Chromium

Isotopes are variants of a particular chemical element, which have the same number of protons but differ in the number of neutrons. Chromium, represented by the chemical symbol 'Cr', has several naturally occurring isotopes, including Cr-50, Cr-52, Cr-53, and Cr-54. The number following 'Cr' denotes the mass number for each isotope, which is the sum of protons and neutrons in the nucleus.
For instance, Cr-50 has a mass number of 50. Since all isotopes of chromium have 24 protons (because the atomic number of chromium is 24), we can deduce that Cr-50 has 26 neutrons (50 - 24). Similar calculations can be done for other chromium isotopes. Each isotope has unique properties and can be found naturally in varying amounts, known as natural abundances.

Protons and Neutrons in Isotopes

In any isotope, the number of protons remains constant and is equivalent to the atomic number of the element. For chromium, this is 24 protons. Understanding neutrons is key to distinguishing between different isotopes of an element. To find the number of neutrons in an isotope, subtract the number of protons from the mass number of that isotope.
In a step-by-step approach, if we examine Cr-53, we subtract the atomic number, which represents protons (24), from the mass number (53), yielding 29 neutrons (53 - 24). This is a fundamental concept that allows us to identify the unique isotopes of any element. Remember that the difference in neutron count influences the isotope's stability and physical properties.

Weighted Average Atomic Mass

The atomic mass listed on the periodic table for any element is not just a simple average of its isotopes' masses. Instead, it's a weighted average, which considers both the mass and the natural abundance of each isotope.
Using chromium as our example, to calculate the atomic mass, we must take each isotope's mass and multiply it by its natural abundance (expressed as a decimal). For Cr-50, we would calculate this by multiplying its mass (49.9460 amu) by its natural abundance (4.345% or 0.04345 when expressed as a decimal), and doing the same for the other isotopes. Summing these products gives us the weighted average atomic mass of chromium, which closely aligns with the standard atomic weight found on the periodic table.