Q30 of 106 Page 384

A parallel beam of light of wavelength 100 nm passes through a sample of atomic hydrogen gas in ground state.

(a) Assume that when a photon supplies some of its energy to a hydrogen atom, the rest of the energy appears as another photon moving in the same direction as the incident photon. Neglecting the light emitted by the excited hydrogen atoms in the directions of the incident beam. What wavelengths may be observed in the transmitted beam?


(b) A radiation detector is placed near the gas to detect radiation coming perpendicular to the incident beam. Find the wavelengths of radiation that may be detected by the detector.


Given: wavelength=100nm


Energy associated with this wavelength



(substituting the vaue of c and plank’s constant)



(a)Suppose En be the energy in the nth orbit. Let consider all possible change in transitions state.


Energy absorbed in transition state in n=1 to n=2



Energy left


Energy left as we know that





Energy absorbed in transition state in n=1 to n=3



Energy left


Energy left




Energy absorbed in transition state in n=3 to n=4



Energy left


Energy left




(b)According to the question if hydrogen atom is radiated perpendicularly then only absorbed energy to change the transition state is taken into consideration.


For n=1 to n=2



And





For n=1 to n=3






For n=3 to n=4






Hence three wavelength obtained are 103nm,121nm,1911nm.


More from this chapter

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28

Radiation coming from transitions n = 2 to n = 1 of hydrogen atoms falls on helium ions in n = 1 and n = 2 states. What are the possible transitions of helium ions as they absorb energy from the radiation?

 29

A hydrogen atom in ground state absorbs a photon of ultraviolet radiation of wavelength 50 nm. Assuming that the entire photon energy is taken up by the electron, with what kinetic energy will the electron be ejected?

 31

A beam of monochromatic light of wavelength λ ejects photoelectrons from a cesium surface (ϕ = 1.9 eV). These photoelectrons are made to collide with hydrogen atoms is ground state. Find the maximum value of λ for which

(a) hydrogen atoms may be ionized,


(b) hydrogen atoms may get excited from the ground state to the first excited state and


(c) the excited hydrogen atoms may emit visible light.


 32

Electrons are emitted from an electron gun at almost zero velocity and are accelerated by an electric filed E through a distance of 1.0 m. The electrons are now scattered by an atomic hydrogen sample in ground state. What should be the minimum value of E so that red light of wavelength 656.3 nm may be emitted by the hydrogen?