Q2P - Organic Chemistry (Mcmurry)

Question

Calculate the amount of energy required to spin-flip a proton in a spectrometer operating at 300 MHz. Does increasing the spectrometer frequency from 200 to 300 MHz increase or decrease the amount of energy necessary for

resonance?

Step-by-Step Solution

Answer

The amount of energy at an operating frequency of 300 MHz is $\frac{{\text{1.20×10}}^{\text{-4}}\text{kJ}}{\text{mol}}$

Increasing the frequency from $\text{200 MHz}$ to $\text{300 MHz}$ increases the amount of energy needed for resonance. 

Step 1: Nuclear Magnetic Resonance Spectroscopy

The original frequency needed for resonance depends on external magnetic field strength, the identity and electronic environment of the nucleus. If a very strong magnetic field is applied, the energy difference between the spin states is larger and high-frequency radiation is required for a spin-flip.

Step 2: Converting the given frequency into units in option (a)

The spectrometer frequency is 300 MHz. 

300 MHz is equal to 3.0x10⁸  Hz.

The wavelength can be found as:

$\begin{array}{c}\text{λ=}\frac{\text{c}}{\text{ν}}\\ \text{=}\frac{{\text{3×10}}^{\text{8}}}{{\text{3.0×10}}^{\text{8}}\text{Hz}}\\ \text{=1.0m}\end{array}$

The energy can be found as:

$\begin{array}{c}\text{E=}\frac{\frac{{\text{1.20×10}}^{\text{-4}}\text{kJ}}{\text{mol}}}{\text{1.0}}\\ \text{=}\frac{{\text{1.20×10}}^{\text{-4}}\text{kJ}}{\text{mol}}\end{array}$

The amount of energy at an operating frequency of 300 HMz is $\frac{{\text{1.20×10}}^{\text{-4}}\text{kJ}}{\text{mol}}$

The wavelength for 200MHz can be given as:

$\begin{array}{c}\text{λ=}\frac{\text{c}}{\text{ν}}\\ \text{=}\frac{{\text{3×10}}^{\text{8}}}{{\text{2.0×10}}^{\text{8}}\text{Hz}}\\ \text{=1.5m}\end{array}$

The energy can be found as:

$\begin{array}{c}\text{E=}\frac{\frac{{\text{1.20×10}}^{\text{-4}}\text{kJ}}{\text{mol}}}{\text{1.5}}\\ \text{=}\frac{{\text{8×10}}^{\text{-5}}\text{kJ}}{\text{mol}}\end{array}$

Increasing the frequency from 200 MHz to 300 MHz increases the amount of energy needed for resonance.