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A PMR spectrometer operates at 300 MHz. Find the value of the magnetic field.
Given: gN = 5.585 and BN = 5.05 x 10-27 JT-I.
Given: gN = 5.585 and BN = 5.05 x 10-27 JT-I.
Correct answer is between '7.02,7.05'. Can you explain this answer?
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A PMR spectrometer operates at 300 MHz. Find the value of the magnetic...
According this formula of frequency:
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A PMR spectrometer operates at 300 MHz. Find the value of the magnetic...
Solution:
To find the magnetic field, we can use the equation:
ω = γB₀
where ω is the Larmor frequency (in radians per second), γ is the gyromagnetic ratio (in radians per second per tesla), and B₀ is the magnetic field strength (in tesla).
We are given that the PMR spectrometer operates at 300 MHz, which corresponds to a Larmor frequency of:
ω = 2πf = 2π(300 × 10⁶) = 1.884 × 10⁹ rad/s
We are also given that gN = 5.585 and BN = 5.05 × 10⁻²⁷ JT⁻¹. The gyromagnetic ratio is related to gN and BN by the equation:
γ = gNμN/ħ
where μN is the nuclear magneton (5.0508 × 10⁻²⁷ JT⁻¹) and ħ is the reduced Planck constant (1.0546 × 10⁻³⁴ J s). Substituting the given values, we get:
γ = (5.585)(5.0508 × 10⁻²⁷)/(1.0546 × 10⁻³⁴) = 2.675 × 10⁸ rad/sT
Now we can rearrange the equation ω = γB₀ to solve for B₀:
B₀ = ω/γ = (1.884 × 10⁹)/(2.675 × 10⁸) = 7.044 T
Therefore, the value of the magnetic field is between 7.02 T and 7.05 T.
To find the magnetic field, we can use the equation:
ω = γB₀
where ω is the Larmor frequency (in radians per second), γ is the gyromagnetic ratio (in radians per second per tesla), and B₀ is the magnetic field strength (in tesla).
We are given that the PMR spectrometer operates at 300 MHz, which corresponds to a Larmor frequency of:
ω = 2πf = 2π(300 × 10⁶) = 1.884 × 10⁹ rad/s
We are also given that gN = 5.585 and BN = 5.05 × 10⁻²⁷ JT⁻¹. The gyromagnetic ratio is related to gN and BN by the equation:
γ = gNμN/ħ
where μN is the nuclear magneton (5.0508 × 10⁻²⁷ JT⁻¹) and ħ is the reduced Planck constant (1.0546 × 10⁻³⁴ J s). Substituting the given values, we get:
γ = (5.585)(5.0508 × 10⁻²⁷)/(1.0546 × 10⁻³⁴) = 2.675 × 10⁸ rad/sT
Now we can rearrange the equation ω = γB₀ to solve for B₀:
B₀ = ω/γ = (1.884 × 10⁹)/(2.675 × 10⁸) = 7.044 T
Therefore, the value of the magnetic field is between 7.02 T and 7.05 T.
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A PMR spectrometer operates at 300 MHz. Find the value of the magnetic field.Given: gN = 5.585 and BN = 5.05 x 10-27 JT-I.Correct answer is between '7.02,7.05'. Can you explain this answer?
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