Concept:The Compton shift calculates the change in a photon's wavelength after colliding with an electron, heavily dependent on the scattering angle \( \theta \).
Formula:$$ \Delta\lambda = \frac{h}{m_0 c}(1-\cos\theta) $$
Solution:- To maximize the shift \( \Delta\lambda \), the expression \( (1-\cos\theta) \) must be maximized.
- The cosine function reaches its minimum mathematical value of -1 at an angle of \( 180^\circ \).
- Substitute this in: \( 1 - (-1) = 2 \).
- This represents a direct head-on collision where the photon bounces straight back, yielding the maximum possible energy transfer to the electron and maximum wavelength shift.
Why other options are incorrect:At \( 0^\circ \), \( \cos(0)=1 \) yielding zero shift. At \( 90^\circ \), \( \cos(90)=0 \) yielding a standard shift of exactly one Compton wavelength, which is half of the maximum possible shift.
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