Question

A compound gives two fragments in a mass spectrometer. They are C₁₉H₇N⁺ and C₁₉H₅0⁺. To separate peaks due to these fragments the instrument should have a resolution of

• A. They cannot be separated
• B. 2.417 x 10^-2
• C. 3.402 × 10⁴
• D. 1.042 × 10⁴

Answer 1

The Correct Option is D

The mass spectrometer peaks given in the question are associated with two fragments, namely, C₁₉H₇N⁺ and C₁₉H₅O⁺. The goal is to determine the resolution required for the instrument to distinguish between these two peaks.

The resolution \(R\) in mass spectrometry is defined as:

\(R = \frac{m}{\Delta m}\) 

where:

• \(m\) is the average mass of the two fragments.
• \(\Delta m\) is the difference in mass between the fragments.

First, calculate the mass of each fragment:

• For C₁₉H₇N⁺:
  • Carbon (C): 19 atoms × 12.01 u = 228.19 u
  • Hydrogen (H): 7 atoms × 1.008 u = 7.056 u
  • Nitrogen (N): 1 atom × 14.01 u = 14.01 u
  • Total mass = 228.19 + 7.056 + 14.01 = 249.256 u
• For C₁₉H₅O⁺:
  • Carbon (C): 19 atoms × 12.01 u = 228.19 u
  • Hydrogen (H): 5 atoms × 1.008 u = 5.04 u
  • Oxygen (O): 1 atom × 16.00 u = 16.00 u
  • Total mass = 228.19 + 5.04 + 16.00 = 249.23 u

The average mass, \(m\), is:

\(m = \frac{249.256 + 249.23}{2} = 249.243 u\)

The difference in mass, \(\Delta m\), is:

\(\Delta m = 249.256 - 249.23 = 0.026 u\)

Now, calculate the required resolution:

\(R = \frac{249.243}{0.026} \approx 9586.2692\)

The closest higher resolution given in the options, which allows for the separation, is \(1.042 \times 10^{4}\).

Therefore, the correct answer is:

1.042 × 10⁴