Find the minimum magnetic field needed for the Zeeman effect to be observed
in a spectral line of 400 nm wavelength when a spectrometer whose resolution
is 0.01nm is used.
We know that
ν=cλ\nu=\frac{c}{\lambda}ν=λc
ν=3×108400×10−9=7.5×10−14Hz\nu=\frac{3\times10^8}{400\times10^{-9}}=7.5\times10^{-14}Hzν=400×10−93×108=7.5×10−14Hz
Again
ν1=cλ1\nu_1=\frac{c}{\lambda_1}ν1=λ1c
ν1=3×108400×10−9+0.010×10−9\nu_1=\frac{3\times10^8}{400\times10^{-9}+0.010\times10^{-9}}ν1=400×10−9+0.010×10−93×108
ν1=3×108400×10−9×11+0.1400\nu_1=\frac{3\times10^8}{400\times10^{-9}}\times\frac{1}{1+\frac{0.1}{400}}ν1=400×10−93×108×1+4000.11
∆ν=7.5×1014(1−2.5×10−5)∆\nu=7.5\times10^{14}(1-2.5\times10^{-5})∆ν=7.5×1014(1−2.5×10−5)
∆ν=1.875×1010Hz∆\nu=1.875\times10^{10}Hz∆ν=1.875×1010Hz
Magnetic field
B=4πm∆νeB=\frac{4\pi m∆\nu}{e}B=e4πm∆ν
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