Problem 5 - Clinical Chemistry

Question

One of the calcium isotopes \(\left({ }^{40} \mathrm{Ca}\right)\) has an atomic weight of \(40 .\) At what positions in a mass spectrum would singly and doubly charged ions of this isotope of calcium appear? Assume that singly charged Ca is listed first. a. 40 and 20 b. 40 and 60 c. 40 and 80 d. 40 and 40

Step-by-Step Solution

Answer

Option a. 40 and 20

Step 1: Understand the Problem

Determine the positions in the mass spectrum for singly and doubly charged ions of the \(^{40} Ca\) isotope.

Step 2: Define Singly Charged Ion

For a singly charged ion, the charge (q) is +1. The position or mass-to-charge ratio (\(m/z\)) on the spectrum is simply the mass of the ion divided by 1. Thus, for \(^{40} Ca^{+}\), \(m/z = 40/1 = 40\).

Step 3: Define Doubly Charged Ion

For a doubly charged ion, the charge (q) is +2. The position or mass-to-charge ratio (\(m/z\)) on the spectrum will be the mass divided by 2. Therefore, for \(^{40} Ca^{2+}\), \(m/z = 40/2 = 20\).

Step 4: Identify the Correct Option

Compare the positions calculated with the given options. Singly charged ion at \(40\) and doubly charged ion at \(20\) matches option (a).

Key Concepts

Singly Charged Ion

In mass spectrometry, ions are detected based on their mass-to-charge ratio, often abbreviated as m/z. A singly charged ion is an ion that has lost or gained one electron.
This kind of ion has a single positive or negative charge (indicated as +1 or -1). Let's consider the calcium isotope \({ }^{40} Ca\) discussed in the exercise.
When it becomes singly charged, it gains a single positive charge, becoming \({ }^{40} Ca^{+}\).
To find the position of this ion in a mass spectrum, we calculate the mass-to-charge ratio \((m/z)\).
For a singly charged ion, the ratio is simply the mass of the ion divided by its charge. In mathematical terms:
\[ m/z = \frac {mass} {charge} \]
For \({ }^{40} Ca^{+}\), the mass-to-charge ratio is:
\[ m/z = \frac {40} {1} = 40 \]
Therefore, the singly charged \({ }^{40} Ca^{+}\) will appear at position 40 on the mass spectrum.

Doubly Charged Ion

A doubly charged ion, as the name suggests, has lost or gained two electrons, giving it a charge of +2 or -2.
The exercise focuses on the calcium isotope \({ }^{40} Ca\) becoming a doubly charged ion, represented as \({ }^{40} Ca^{2+} \).
The mass-to-charge (m/z) ratio changes when the ion is doubly charged because the charge is now 2. Again, we use the formula:
\[ m/z = \frac {mass} {charge} \]
For the doubly charged \({ }^{40} Ca^{2+}\), the calculation would be:
\[ m/z = \frac {40} {2} = 20 \]
This means that the doubly charged \({ }^{40} Ca\) ion, \({ }^{40} Ca^{2+}\), will appear at position 20 in the mass spectrum.

Mass-to-Charge Ratio

The mass-to-charge ratio, abbreviated as m/z, is a crucial concept in mass spectrometry.
It is calculated by dividing the mass of the ion (often measured in atomic mass units, or amu) by its charge (represented in units of elementary charge, e).
Here's the basic formula:
\[ \frac{m}{z} \]
Imagine you have an ion with a mass of 40 amu and a charge of +1 e (a singly charged ion). The m/z ratio would be:
\[ m/z = \frac {40} {1} = 40 \]
Now, if the same ion has a charge of +2 e (a doubly charged ion), the m/z ratio changes:
\[ m/z = \frac {40} {2} = 20 \]
This ratio helps in identifying the relative abundance and type of ions present in a sample. By understanding the m/z ratio, scientists can accurately interpret the results of a mass spectrometry analysis.