Problem 100 - Chemistry: The Central Science

Question

The Chemistry and Life box in Section 6.7 described the techniques called NMR and MRI. (a) Instruments for obtaining MRI data are typically labeled with a frequency, such as 600 MHz. In what region of the electromagnetic spectrum does a photon with this frequency belong? (b) What is the value of \(\Delta E\) in Figure 6.27 that would correspond to the absorption of a photon of radiation with frequency \(450 \mathrm{MHz} ?(\mathbf{c})\) When the 450 -MHz photon is absorbed, does it change the spin of the electron or the proton on a hydrogen atom?

Step-by-Step Solution

Answer

(a) A photon with a frequency of 600 MHz belongs to the radio wave region of the electromagnetic spectrum, specifically in the UHF (Ultra High Frequency) band. (b) The energy change (∆E) for the absorption of a photon with a frequency of 450 MHz is 2.982 × 10⁻²⁵ J. (c) The absorption of a 450 MHz photon changes the spin of the proton, not the electron, on a hydrogen atom.

Step 1: (a) Determine photon energy and spectrum region

First, we need to determine the energy of a photon with a frequency of 600 MHz. Use the formula: \[E = h\nu\] Where \(E\) is the photon energy, \(h\) is the Planck's constant (\(6.626 \times 10^{-34} \mathrm{J\:s}\)), and \(\nu\) is the frequency. Remember to change MHz to Hz by multiplying by \(10^{6}\). \[E = (6.626 \times 10^{-34} \mathrm{J\:s}) (600 \times 10^{6} \mathrm{Hz})\] \[E = 3.976 \times 10^{-25} \mathrm{J}\] Now, we need to determine the region in the electromagnetic spectrum where this energy belongs. The 600 MHz frequency corresponds to radio waves, specifically, it falls in the UHF (Ultra High Frequency) band.

Step 2: (b) Calculate energy change for the 450 MHz photon

Now we need to calculate the energy change (\(\Delta E\)) for the absorption of a photon with a frequency of 450 MHz. Use the same formula: \[\Delta E = h\nu\] \[\Delta E = (6.626 \times 10^{-34} \mathrm{J\:s}) (450 \times 10^{6} \mathrm{Hz})\] \[\Delta E = 2.982 \times 10^{-25} \mathrm{J}\]

Step 3: (c) Determine the effect of the 450 MHz photon on electron or proton spin

Nuclear Magnetic Resonance (NMR) and Magnetic Resonance Imaging (MRI) techniques are based on the interaction of photons with nuclei (protons), not electrons. When a photon is absorbed, it affects the spin states of nuclei (protons) in the magnetic field. Thus, the absorption of a 450 MHz photon changes the spin of the proton, not the electron, on a hydrogen atom.