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The Zeeman effect refers to the splitting of a spectral line into multiple components in the presence of a magnetic field. This happens due to the interaction between the magnetic field and the magnetic moment associated with the angular momentum of electrons.

The frequency shift (frequencyshift) caused by the Zeeman effect is given by the formula \[ \Delta f = \dfrac{e B}{4 \pi m} \] where \( e \) is the electron charge (~1.6 × 10^{-19} C), \( B \) is the magnetic field strength (0.3 T), and \( m \) is the electron mass (~9.11 × 10^{-31} kg). Substituting the values, we get: \[ \Delta f = \dfrac{(1.6 \times 10^{-19} \ ext{C})(0.3 \ ext{T})}{4 \pi (9.11 \times 10^{-31} \ ext{kg})} \approx 1.4 \times 10^{10} \ ext{Hz} \]

The change in wavelength \(\Delta \lambda\) can be found using the relation between frequency and wavelength: \(c = \lambda f\), where \(c\) is the speed of light (\(3 \times 10^{8} \ ext{m/s}\)).The change in frequency can be related to change in wavelength as: \[ \Delta \lambda = \dfrac{c \cdot \Delta f}{f^2} \approx \dfrac{c}{f^2} \cdot \dfrac{e B \lambda}{4 \pi m} \] For an incident wavelength \(\lambda = 630.25 \ ext{nm} = 630.25 \times 10^{-9} \ ext{m}\), and using the frequency before split: \[ f = \dfrac{c}{\lambda} = \dfrac{3 \times 10^{8}}{630.25 \times 10^{-9}} \approx 4.75 \times 10^{14} \ ext{Hz}\] \[ \Delta \lambda = \dfrac{(3 \times 10^8)(630.25 \times 10^{-9})(1.4 \times 10^{10})}{(4.75 \times 10^{14})^2} \approx 14.2 \times 10^{-12} \text{m} \] Thus \( \Delta \lambda \approx 14.2 \ ext{pm} \).

To find the fractional change in wavelength: \[ \text{Fractional Change} = \dfrac{\Delta \lambda}{\lambda} = \dfrac{14.2 \times 10^{-12}}{630.25 \times 10^{-9}} \approx 2.25 \times 10^{-5} \] So, the wavelength changes by approximately 0.00225%.