1Physics 316Solution for quiz 1Spring 2005Cornell UniversitySteve DrascoI.EXERCISE 1We know from Wein’s displacement law thatνmax∝T. ThereforeT→T/3 means thatνmax→νmax/3 = 117THz. We know from Stefan’s law thatP∝T4. ThereforeT→T/3 means thatP→P/81 = 12.3 W.II.EXERCISE 2We will use conservation of energy.The total initial energy is only the kinetic energy of the electronEi=Ke.The total final energy is that of the photon plus the potential energy of the now bound electronEf=hνmax-W.EquatingEiandEfgivesνmax= (Ke+W)/h.III.EXERCISE 3A photon emitted after a change from levelnitonfhas energyhν∝n-2f-n-2i. For the first Balmer linenf= 2andni= 3. For the first Lyman linenf= 1 andni= 2. So if the frequency of the first Lyman line isνLthenhνLhνB=1-1/41/4-1/9=3/49/36-4/36=34365=275,(3.1)which means thatνL= (27/5)νB= 2470 THz.IV.EXERCISE 4Sinceλ=h/p, andp=mv, we havev=h/(mλ). Usingh= 6.6×10-34Js, from the textbook givesv=6.
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