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The magnetic field (in Tesla) required for flipping a 1H nucleus in an NMR spectrometer operating at 400 MHz is _______ [Given: g = 2.67 × 108 T–1 s–1, π = 3.14]
Correct answer is between '9,10'. Can you explain this answer?
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The magnetic field (in Tesla) required for flipping a 1H nucleus in an...
Given:
- NMR spectrometer operating at 400 MHz
- g = 2.67 x 10^8 T1 s1
- θ = 3.14
To find:
The magnetic field required for flipping a 1H nucleus in the NMR spectrometer.
Solution:
The resonance frequency in Nuclear Magnetic Resonance (NMR) is given by the Larmor equation:
ω = γB
Where:
ω is the resonance frequency
γ is the gyromagnetic ratio
B is the magnetic field strength
In this case, we need to find the magnetic field strength B required for a 1H nucleus with a resonance frequency of 400 MHz.
Step 1: Convert the resonance frequency from MHz to Hz:
400 MHz = 400 x 10^6 Hz
Step 2: Substitute the values into the Larmor equation to find the gyromagnetic ratio γ:
400 x 10^6 Hz = γB
Step 3: Rearrange the equation to solve for γ:
γ = (400 x 10^6 Hz) / B
Step 4: Substitute the given values for γ and solve for B:
2.67 x 10^8 T^-1 s^-1 = (400 x 10^6 Hz) / B
Step 5: Rearrange the equation to solve for B:
B = (400 x 10^6 Hz) / (2.67 x 10^8 T^-1 s^-1)
Step 6: Simplify the equation:
B = 1.498 T
The magnetic field required for flipping a 1H nucleus in the NMR spectrometer is 1.498 Tesla.
Conclusion:
The correct answer is between '1.49' and '1.50'.
- NMR spectrometer operating at 400 MHz
- g = 2.67 x 10^8 T1 s1
- θ = 3.14
To find:
The magnetic field required for flipping a 1H nucleus in the NMR spectrometer.
Solution:
The resonance frequency in Nuclear Magnetic Resonance (NMR) is given by the Larmor equation:
ω = γB
Where:
ω is the resonance frequency
γ is the gyromagnetic ratio
B is the magnetic field strength
In this case, we need to find the magnetic field strength B required for a 1H nucleus with a resonance frequency of 400 MHz.
Step 1: Convert the resonance frequency from MHz to Hz:
400 MHz = 400 x 10^6 Hz
Step 2: Substitute the values into the Larmor equation to find the gyromagnetic ratio γ:
400 x 10^6 Hz = γB
Step 3: Rearrange the equation to solve for γ:
γ = (400 x 10^6 Hz) / B
Step 4: Substitute the given values for γ and solve for B:
2.67 x 10^8 T^-1 s^-1 = (400 x 10^6 Hz) / B
Step 5: Rearrange the equation to solve for B:
B = (400 x 10^6 Hz) / (2.67 x 10^8 T^-1 s^-1)
Step 6: Simplify the equation:
B = 1.498 T
The magnetic field required for flipping a 1H nucleus in the NMR spectrometer is 1.498 Tesla.
Conclusion:
The correct answer is between '1.49' and '1.50'.
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