Question

Q. show that ∆E/E = hf’/moc2(1-cos ө )

Answer 1

Answer on Question #58657-Physics-Quantum Mechanics

Q. show that $\Delta E / E = h f^{\prime} / \mathrm{moc2}(1 - \cos \theta)$

Solution

$$\lambda^ {\prime} = \lambda + \frac {h}{m _ {e} c} (1 - \cos \theta)$$ $$E ^ {\prime} = \frac {\mathrm {h c}}{\lambda^ {\prime}}; E = \frac {\mathrm {h c}}{\lambda}.$$ $$\frac {\Delta \mathrm {E}}{\mathrm {E}} = \frac {\frac {\mathrm {h c}}{\lambda^ {\prime}} - \frac {\mathrm {h c}}{\lambda}}{\frac {\mathrm {h c}}{\lambda}} = \frac {\lambda - \lambda^ {\prime}}{\lambda^ {\prime}} = \frac {- \frac {h}{m _ {e} c} (1 - \cos \theta)}{\frac {c}{f ^ {\prime}}} = - \frac {h f ^ {\prime}}{m _ {e} c ^ {2}} (1 - \cos \theta)$$ $$\left| \frac {\Delta \mathrm {E}}{\mathrm {E}} \right| = \frac {h f ^ {\prime}}{m _ {e} c ^ {2}} (1 - \cos \theta)$$

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