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| 1. |
Find the velocity of the excited hydrogen atoms if the first line of the Lyman series is displaced by Delta lambda= 0.20 nm when their radiation is observed at an angle theta=45^(@) to their motion direction. |
| Answer» <html><body><p></p>Solution :Since `<a href="https://interviewquestions.tuteehub.com/tag/delta-947703" style="font-weight:bold;" target="_blank" title="Click to know more about DELTA">DELTA</a> lambda(= 0.20nm)lt lt lambda(= 121nm)` of the first <a href="https://interviewquestions.tuteehub.com/tag/lyman-545655" style="font-weight:bold;" target="_blank" title="Click to know more about LYMAN">LYMAN</a> line of `H` atom, we need not worry about `V^(<a href="https://interviewquestions.tuteehub.com/tag/2-283658" style="font-weight:bold;" target="_blank" title="Click to know more about 2">2</a>)//c^(2)` effects. Then <br/> `omega'=(omega)/(1-betacos theta),beta=(v)/(c )` <br/> Hence `1- beta <a href="https://interviewquestions.tuteehub.com/tag/cos-935872" style="font-weight:bold;" target="_blank" title="Click to know more about COS">COS</a> theta=(omega)/(omega')=(lambda')/(lambda)` <br/> or `beta cos theta=1-(lambda')/(lambda)=(Delta lambda)/(lambda)` <br/> But `omega=(3)/(4)R so lambda=(2pic)/(omega)=(8pic)/(<a href="https://interviewquestions.tuteehub.com/tag/3r-311113" style="font-weight:bold;" target="_blank" title="Click to know more about 3R">3R</a>)` <br/> Hence `v=cbeta=(3RDeltalambda)/(8pi cos theta)` <br/> Substitution gives `( cos theta=(1)/(sqrt(2)))` <br/> `v= 7.0xx10^(5)m//s`</body></html> | |