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The 1H NMR frequency at 1.0 T is 72.4 MHz. If the gyromagnetic ratios of 1H and 13C are 24 x 107 and 6 x 107 T1s-1, respectively. The 13C frequency at 1.0 T is ______ MHz. (Round off to one decimal place).
Correct answer is between '17.9,18.3'. Can you explain this answer?
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The 1H NMR frequency at 1.0 T is 72.4 MHz. If the gyromagnetic ratios ...
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The 1H NMR frequency at 1.0 T is 72.4 MHz. If the gyromagnetic ratios ...
Given:
- 1H NMR frequency at 1.0 T = 72.4 MHz
- Gyromagnetic ratio of 1H (γ1H) = 24 x 10^7 T^(-1)s^(-1)
- Gyromagnetic ratio of 13C (γ13C) = 6 x 10^7 T^(-1)s^(-1)
To Find:
- 13C frequency at 1.0 T
Solution:
The gyromagnetic ratio (γ) relates the magnetic moment of a particle to its angular momentum. It is given by the equation:
γ = μ / J
Where:
- γ is the gyromagnetic ratio
- μ is the magnetic moment
- J is the angular momentum
The angular momentum of a particle is given by the equation:
J = Iω
Where:
- J is the angular momentum
- I is the moment of inertia
- ω is the angular velocity
In NMR spectroscopy, the gyromagnetic ratio is used to calculate the resonance frequency of a nucleus in a magnetic field.
Step 1: Calculate the magnetic moment of 1H:
Given: γ1H = 24 x 10^7 T^(-1)s^(-1)
The magnetic moment of 1H is given by:
μ1H = γ1H * J1H
The angular momentum of 1H is given by:
J1H = I1H * ω
Since I1H is a constant, let's assume it as 1 for simplicity.
J1H = 1 * ω
Assuming the angular velocity ω as 1 for simplicity, we can rewrite the equation as:
J1H = 1 * 1 = 1
Substituting the values:
μ1H = γ1H * J1H
μ1H = 24 x 10^7 T^(-1)s^(-1) * 1
μ1H = 24 x 10^7 T^(-1)s^(-1)
Step 2: Calculate the magnetic moment of 13C:
Given: γ13C = 6 x 10^7 T^(-1)s^(-1)
Using the same approach as above, the magnetic moment of 13C is given by:
μ13C = γ13C * J13C
J13C = I13C * ω
Assuming I13C as 1 and ω as 1, we can calculate J13C as:
J13C = 1 * 1 = 1
Substituting the values:
μ13C = γ13C * J13C
μ13C = 6 x 10^7 T^(-1)s^(-1) * 1
μ13C = 6 x 10^7 T^(-1)s^(-1)
Step 3: Calculate the 13C frequency at 1.0 T:
The frequency of a nucleus in a magnetic field is given by the Larmor equation:
ν = γB
Where:
- ν is the frequency
- γ is the gyromagnetic ratio
- B is the magnetic field strength
Given: B = 1.0 T
- 1H NMR frequency at 1.0 T = 72.4 MHz
- Gyromagnetic ratio of 1H (γ1H) = 24 x 10^7 T^(-1)s^(-1)
- Gyromagnetic ratio of 13C (γ13C) = 6 x 10^7 T^(-1)s^(-1)
To Find:
- 13C frequency at 1.0 T
Solution:
The gyromagnetic ratio (γ) relates the magnetic moment of a particle to its angular momentum. It is given by the equation:
γ = μ / J
Where:
- γ is the gyromagnetic ratio
- μ is the magnetic moment
- J is the angular momentum
The angular momentum of a particle is given by the equation:
J = Iω
Where:
- J is the angular momentum
- I is the moment of inertia
- ω is the angular velocity
In NMR spectroscopy, the gyromagnetic ratio is used to calculate the resonance frequency of a nucleus in a magnetic field.
Step 1: Calculate the magnetic moment of 1H:
Given: γ1H = 24 x 10^7 T^(-1)s^(-1)
The magnetic moment of 1H is given by:
μ1H = γ1H * J1H
The angular momentum of 1H is given by:
J1H = I1H * ω
Since I1H is a constant, let's assume it as 1 for simplicity.
J1H = 1 * ω
Assuming the angular velocity ω as 1 for simplicity, we can rewrite the equation as:
J1H = 1 * 1 = 1
Substituting the values:
μ1H = γ1H * J1H
μ1H = 24 x 10^7 T^(-1)s^(-1) * 1
μ1H = 24 x 10^7 T^(-1)s^(-1)
Step 2: Calculate the magnetic moment of 13C:
Given: γ13C = 6 x 10^7 T^(-1)s^(-1)
Using the same approach as above, the magnetic moment of 13C is given by:
μ13C = γ13C * J13C
J13C = I13C * ω
Assuming I13C as 1 and ω as 1, we can calculate J13C as:
J13C = 1 * 1 = 1
Substituting the values:
μ13C = γ13C * J13C
μ13C = 6 x 10^7 T^(-1)s^(-1) * 1
μ13C = 6 x 10^7 T^(-1)s^(-1)
Step 3: Calculate the 13C frequency at 1.0 T:
The frequency of a nucleus in a magnetic field is given by the Larmor equation:
ν = γB
Where:
- ν is the frequency
- γ is the gyromagnetic ratio
- B is the magnetic field strength
Given: B = 1.0 T
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The 1H NMR frequency at 1.0 T is 72.4 MHz. If the gyromagnetic ratios of 1H and 13C are 24 x 107 and 6 x 107 T1s-1, respectively. The 13C frequency at 1.0 T is ______ MHz. (Round off to one decimal place).Correct answer is between '17.9,18.3'. Can you explain this answer?
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The 1H NMR frequency at 1.0 T is 72.4 MHz. If the gyromagnetic ratios of 1H and 13C are 24 x 107 and 6 x 107 T1s-1, respectively. The 13C frequency at 1.0 T is ______ MHz. (Round off to one decimal place).Correct answer is between '17.9,18.3'. Can you explain this answer? for Chemistry 2024 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about The 1H NMR frequency at 1.0 T is 72.4 MHz. If the gyromagnetic ratios of 1H and 13C are 24 x 107 and 6 x 107 T1s-1, respectively. The 13C frequency at 1.0 T is ______ MHz. (Round off to one decimal place).Correct answer is between '17.9,18.3'. Can you explain this answer? covers all topics & solutions for Chemistry 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The 1H NMR frequency at 1.0 T is 72.4 MHz. If the gyromagnetic ratios of 1H and 13C are 24 x 107 and 6 x 107 T1s-1, respectively. The 13C frequency at 1.0 T is ______ MHz. (Round off to one decimal place).Correct answer is between '17.9,18.3'. Can you explain this answer?.
The 1H NMR frequency at 1.0 T is 72.4 MHz. If the gyromagnetic ratios of 1H and 13C are 24 x 107 and 6 x 107 T1s-1, respectively. The 13C frequency at 1.0 T is ______ MHz. (Round off to one decimal place).Correct answer is between '17.9,18.3'. Can you explain this answer? for Chemistry 2024 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about The 1H NMR frequency at 1.0 T is 72.4 MHz. If the gyromagnetic ratios of 1H and 13C are 24 x 107 and 6 x 107 T1s-1, respectively. The 13C frequency at 1.0 T is ______ MHz. (Round off to one decimal place).Correct answer is between '17.9,18.3'. Can you explain this answer? covers all topics & solutions for Chemistry 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The 1H NMR frequency at 1.0 T is 72.4 MHz. If the gyromagnetic ratios of 1H and 13C are 24 x 107 and 6 x 107 T1s-1, respectively. The 13C frequency at 1.0 T is ______ MHz. (Round off to one decimal place).Correct answer is between '17.9,18.3'. Can you explain this answer?.
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