Modern Physics 7 Question 50

56. 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 V. Calculate the work function of the metal, and the stopping potential for the photoelectrons ejected by the longer wavelength (Rydberg’s constant =1.094×107m1 )

(1990,7M)

Show Answer

Answer:

Correct Answer: 56. 2eV,0.74V

Solution:

  1. The stopping potential for shorter wavelength is 3.95V i.e. maximum kinetic energy of photoelectrons corresponding to shorter wavelength will be 3.95eV. Further energy of incident photons corresponding to shorter wavelength will be in transition from n=4 to n=3.

E43=E4E3=(13.6)(3)2(4)2(13.6)(3)2(3)2=5.95eV

Now, from the equation,

Kmax=EW we have W=EKmax=E43Kmax=(5.953.95)eV=2eV

Longer wavelength will correspond to transition from n=5 to n=4. From the relation,

1λ=Rz21Nf21Ni2

The longer wavelength,

or

1λ=(1.094×107)(3)3116125λ=4.514×107m=4514\AA

Energy corresponding to this wavelength,

E=12375eV\AA4514\AA=2.74eV

Maximum kinetic energy of photo-electrons

Kmax=EW=(2.742)eV=0.74eV

or the stoping potential is 0.74V.



जेईई के लिए मॉक टेस्ट

एनसीईआरटी अध्याय वीडियो समाधान

दोहरा फलक