Question

Radiation in the radiofrequency region of the electromagnetic spectrum for use in NMR is often described in terms of frequency, in units of MHz. One common example is ¹H resonance frequency at 2.35T, which is 100.0MHz (1.000 x 10⁸Hz). Calculate the values of its angular frequency (ω) in rad/s or s^-1, wavenumber (ν̅ ) in cm^-1, wavelength (λ) in m, and energy (E) in J.

Answer 1

angular frequency (ω) =(2)x(3.14)(resonance frequency)

= 2*3.14*10^8

= 6.28 x 10^8 rad/s

Angular wavenumber k = angular frequency / speed of light

= 6.28 x 10^8/3 x 10^8

= 2.093 m-1 x 1m/100cm

= 0.0209 cm-1

Wavelength λ = 2 x 3.14/k

= 2 x 3.14/0.0209

= 300.47 cm x 1m/100cm

= 3 m

Energy E = h x c / λ

= 6.6*10^-34 J-s x 3 x 10^8 m/s / 3 m

= 6.6 x 10^-26 J