Answer to Question #279270 in Atomic and Nuclear Physics for BIGIRIMANA Elie

Question #279270

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.

1
Expert's answer
2021-12-15T22:33:19-0500

We know that

ν=cλ\nu=\frac{c}{\lambda}

ν=3×108400×109=7.5×1014Hz\nu=\frac{3\times10^8}{400\times10^{-9}}=7.5\times10^{-14}Hz

Again

ν1=cλ1\nu_1=\frac{c}{\lambda_1}

ν1=3×108400×109+0.010×109\nu_1=\frac{3\times10^8}{400\times10^{-9}+0.010\times10^{-9}}

ν1=3×108400×109×11+0.1400\nu_1=\frac{3\times10^8}{400\times10^{-9}}\times\frac{1}{1+\frac{0.1}{400}}

ν=7.5×1014(12.5×105)∆\nu=7.5\times10^{14}(1-2.5\times10^{-5})

ν=1.875×1010Hz∆\nu=1.875\times10^{10}Hz

Magnetic field

B=4πmνeB=\frac{4\pi m∆\nu}{e}


B=4×3.14×9.1×1031×1.875×10101.06×1019=1.34TB=\frac{4\times3.14\times9.1\times10^{-31}\times1.875\times10^{10}}{1.06\times10^{-19}}=1.34T


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