Atoms And Nuclei Question 310

Question: Electrons in hydrogen like atom (Z=3) make transitions from the fifth to the fourth orbit and from the fourth to the third orbit. The resulting radiations are incident normally on a metal plate and eject photoelectrons. The stopping potential for the photoelectrons ejected by the shorter wavelength is 3.95 volts. Find the stopping potential for the photoelectrons ejected by the longer wavelength, then. (Rydberg constant)

Options:

A) 5V

B) 2V

C) 0.754 V

D) 2.99V

Show Answer

Answer:

Correct Answer: C

Solution:

  • For transition from n=5 to n=4,

    hv=13.6×9[116125]=13.6×9×916×25=2.754eV

    For transition from n=4 to n=3, hv=13.6×9[19116]=13.6×9×79×16=5.95eV

    For transition n=4 to n=3, the frequency is high and hence wavelength is short.

    For photoelectric effect, hv=W=ev0

    Where W= work function 5.95×1.6×1019W=1.6×1019×3.95
    W=2×1.6×1019=2eV

    Again applying hvW=eV0 We get, 2.754×1.6×10192×1.6×1019= 1.6×1019V0



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