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    ​For a nuclear spin of spin quantum no.  (I=12)(I=\frac {1}{2})(I=21​) processing in a magnetic field at a Larmor frequency of 300 MHz,
    Question

    For a nuclear spin of spin quantum no.  (I=12)(I=\frac {1}{2}) processing in a magnetic field at a Larmor frequency of 300 MHz, the wavelength of incident radiation required to excite the nuclear spins must be approximately:

    A.

    1 nm

    B.

    1cm

    C.

    1m

    D.

    10m

    Correct option is C

    Explanation-

    Given-

    Larmor frequency (ν)=300 MHz=3×108 Hz\textbf{Larmor frequency } (\nu) = 300\,\text{MHz} = 3 \times 10^8\,\text{Hz}

    Formula:
    The wavelength  and frequency  are related by:​​

    λ=cν\lambda = \frac{c}{\nu}

    Where:

    c=3×108 m/s(speed of light)ν=3×108 Hzc = 3 \times 10^8 \,\text{m/s} \quad \text{(speed of light)} \\\nu = 3 \times 10^8 \,\text{Hz}

    Substituting values-

                       λ=3×108 m/s3×108 Hz=1 m\lambda = \frac{3 \times 10^8 \,\text{m/s}}{3 \times 10^8 \,\text{Hz}} = 1\,\text{m}

    So, the correct answer is option c : 1 m

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