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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. Calculate the work function of the metal and the stopping potential for the photoelectrons ejected by the longer wavelength. (Rydberg constant = 1.094 x 10 7 m -1 )

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. Calculate the work function of the metal and the stopping potential for the photoelectrons ejected by the longer wavelength. 
(Rydberg constant  = 1.094 x 107 m-1)

Grade:11

1 Answers

Kevin Nash
askIITians Faculty 332 Points
7 years ago
Hello Student,
Please find the answer to your question
For hydrogen like atom energy of the nth orbit is
En = 13. 6 n2 Z2 eV / atom
For transition from n = 5 to n = 4,
Hv = 13.6 x 9 [1 / 16 – 1 / 25 ] = 13.6 x 9 x 9 / 16 x 25 = 2.754 eV
For transition from n = 4 to n = 3,
hv' = 13. 6 x 9 [ 1/9 – 1 / 16 ] = 13. 6 x 9 x 7 / 9 x 16 = 5.95 eV
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 x 1.6 x 10-19 – W = 1.6 x 10-19 x 3. 95
⇒ W = 2 x 1.6 x 10-19 = 2eV
Again applying hv – W = eV’
We get, 2.754 x 1.6 x 10-19 – 2 x 1.6 x 10-19 = 1.6 x 10-19 V’0
⇒ V0’ = 0.754 V
Thanks
Kevin Nash
askIITians Faculty

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