A photon of wavelength $$\lambda$$ is scattered from an electron, which was at rest. The wavelength shift $$\Delta\lambda$$ is three times of $$\lambda$$ and the angle of scattering $$\theta$$ is 60°. The angle at which the electron recoiled is $$\phi$$. The value of $$\tan \phi$$ is: (electron speed is much smaller than the speed of light)

$$\vec{\Delta p} = \left( \frac{p}{4} \cos 60^\circ \hat{i} + \frac{p}{4} \sin 60^\circ \hat{j} \right) - p\hat{i}$$

$$\vec{\Delta p} = -\frac{7p}{8} \hat{i} + \frac{\sqrt{3}p}{8} \hat{j}$$

$$\Rightarrow \tan\phi = \frac{\frac{\sqrt{3}p}{8}}{\frac{7p}{8}} = \frac{\sqrt{3}}{7}$$

$$\tan\phi \approx 0.25$$

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