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

Verified step by step guidance

1. Identify the relationship between frequency and energy for a nucleus in an NMR spectrometer. The energy difference (\( \Delta E \)) between the nuclear spin states is given by the equation \( \Delta E = h \nu \), where \( h \) is Planck's constant (6.626 \times 10^{-34} \text{ J s}) and \( \nu \) is the frequency of the NMR spectrometer.
2. Convert the frequency from MHz to Hz. Since 1 MHz = 10^6 Hz, multiply 300 MHz by 10^6 to get the frequency in Hz.
3. Substitute the frequency in Hz and Planck's constant into the equation \( \Delta E = h \nu \) to calculate the energy in joules.
4. Convert the energy from joules to calories. Use the conversion factor 1 calorie = 4.184 joules to convert the energy obtained in joules to calories.
5. Ensure the units are consistent and check the calculation steps to verify the energy required to flip the 1H nucleus in the NMR spectrometer.

Key Concepts

Nuclear Magnetic Resonance (NMR)

Nuclear Magnetic Resonance (NMR) is a spectroscopic technique used to observe the magnetic properties of atomic nuclei. In NMR, nuclei in a magnetic field absorb and re-emit electromagnetic radiation, allowing for the determination of molecular structure. The frequency of the NMR spectrometer, measured in megahertz (MHz), indicates the strength of the magnetic field and influences the energy required to flip the nuclear spin states.

Energy Calculation in NMR

The energy required to flip a nucleus in NMR can be calculated using the formula E = hν, where E is energy, h is Planck's constant, and ν is the frequency of the NMR spectrometer. This relationship shows that higher frequencies correspond to higher energy transitions. For a spectrometer operating at 300 MHz, this calculation will yield the energy in joules, which can then be converted to calories for the final answer.

Conversion of Energy Units

In scientific calculations, it is often necessary to convert energy units from joules to calories. The conversion factor is 1 calorie = 4.184 joules. Understanding this conversion is essential for expressing the energy required for the NMR process in the desired units, ensuring clarity and accuracy in the final result.