Question

Calculate the amount of energy (in calories) required to flip an ¹Hnucleus in an NMR spectrometer that operates at 300 MHz.

Short answer

The amount of energy required to flip¹H nucleus is 475.16 X 10^-28

Step-by-step solution

NMR spectroscopy

NMR spectroscopy identifies the carbon-hydrogen framework of an organic compound. The greater the magnetic field produced by the magnet, the greater the operating frequency of the spectrophotometer.

Calculating the amount of energy According to the Max-Planck relationship,

\[E = h\nu \]

Where E is the energy required, h is Planck’s constant, \(\left( {6.627 \times {{10}^{ - 34}}J - S} \right)\) and \(\nu \) is the frequency 300 MHz \(\left( {300 \times {{10}^6}\,{s^{ - 1}}} \right)\).

Upon substituting all the known values in the given equation, we get,

\(\begin{array}{c}E = h\nu \\ = 6.627 \times {10^{ - 34}}J - S \times 300 \times {10^6}\,{s^{ - 1}}\\ = 1988.1 \times {10^{ - 28}}J\end{array}\)

The standard relationship between joule and calorie is as follows:

\(1\,J = 0.2390057\,calories\)

Therefore, \(1988.1 \times {10^{ - 28}}J\) is converted to calories as follows:

\(\begin{array}{c}1\,J = 0.2390057\,calories\\1988.1 \times {10^{ - 28}}J = 1988.1 \times {10^{ - 28}} \times 0.2390057\,calories\\ = 475.16 \times {10^{ - 28}}\,calories\end{array}\)

Thus, the amount of energy required to flip is \(475.16 \times {10^{ - 28}}\,calories\) .