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The total energy of an electron in the ground state of a hydrogen atom is -13.6 eV. The kinetic energy of an electron in the first excited state is: 

  • 3.4 eV

  • 6.8 eV

  • 13.6 eV

  • 13.6 eV


A.

3.4 eV

The total energy of an electron in the orbit is equal to negative of its kinetic energy.
 The energy of hydrogen atom when the electron revolves in nth orbit is 
E = -13.6/n2 eV

In the ground state: n =1

E = - -13.6/12 = -13.6 eV

For n = 2, E  = -13.6/22 = -3.4 eV

so, the kinetic energy of an electron in the first excited state (i,e, for n = 2 ) is
K = - E = - (-3.4) - 3.4 eV

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Ionization potential of hydrogen atom is 13.6 eV. Hydrogen atoms in the ground state are excited by monochromatic radiation of photon energy 12.1 eV. According to Bohr's theory, the spectral lines emitted by hydrogen will be

  • two 

  • three

  • four

  • four


B.

three

Ionization energy corresponding to ionization potential  = -13.6 eV.
Photon energy incident = 12.1 eV
So, the energy of electron in excited state
    = -13.6 + 12.1 = -1.5 eV
i.e.,      

i.e., energy of electron in excited state corresponds to third orbit.
The possible spectral lines are when electron jumps from orbit 3rd to 2nd; 3rd to 1st and 2nd to 1st. Thus, 3 spectral lines are emitted.

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The ratio of kinetic energy to the total energy of an electron in a Bohr orbit of the hydrogen atom, is

  • 1:1

  • 1:-1

  • 1:-2

  • 2:-1


B.

1:-1

In a Bohr orbit of the hydrogen atom Kinetic energy,

k = kze22rnTotal energy, E = -kze22rn

so, Kinetic energy: total energy  = 1:-1


The ratio of wavelengths of the last line of Balmer series and the last line of Lyman series is

  • 2

  • 1

  • 4

  • 4


C.

4

For the last Balmer Series
1 over straight lambda subscript straight b space equals space straight R space open square brackets 1 over 2 squared minus 1 over infinity squared close square brackets

straight lambda subscript straight b space equals space 4 over straight R
For space last space layman space Series
fraction numerator begin display style 1 end style over denominator begin display style straight lambda subscript 1 end style end fraction space equals space straight R space open square brackets fraction numerator begin display style 1 end style over denominator begin display style 1 squared end style end fraction minus fraction numerator begin display style 1 end style over denominator begin display style infinity squared end style end fraction close square brackets
straight lambda subscript 1 space equals space 1 over straight R
straight lambda subscript straight b over straight lambda subscript straight l space equals space fraction numerator begin display style 4 over straight R end style over denominator begin display style 1 over straight R end style end fraction
straight lambda subscript straight b over straight lambda subscript straight l space equals space 4


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A photo-cell employs photoelectric effect to convert

  • change in the frequency of light into a change in electric voltage

  • change in the intensity of illumination into a change in photoelectric current

  • change in the intensity of illumination into a change in the work function of the photocathode

  • change in the intensity of illumination into a change in the work function of the photocathode


B.

change in the intensity of illumination into a change in photoelectric current

In photoelectric effect when monochromatic radiations of suitable frequency fall on the photo-sensitive plate called cathode, the photoelectrons are emitted which get accelerated towards anode. These electrons flow in the outer circuit resulting in the photoelectric current.
Using the incident radiations of a fixed frequency, it is found that the photoelectric current increases linearly with the intensity of incident light as shown in figure. Hence, a photocell employs photoelectric effect to convert change in the intensity of illumination into a change in photoelectric current.

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