Physics

For Paschen Series, $n=3,$ and mimimum wavelength occurs when transition occurs just from series limit,

$λhC =−13.6[n_{1}1 −n_{2}1 ]$

$⇒λ=13.6×[91 −1]−4.14×10_{−15}×3×10_{8} $

$⇒λ=13.6×84.14×10_{−15}×3×10_{8}×9 $

$⇒λ=1.878655×10_{−6}×9×0.04861111$ m

$⇒λ=8.21911×10_{−07}$m

$⇒λ=8219.11×10_{−10}$ m

$⇒λ=8219A_{∘}≈8181A_{∘}$

The graphs published by Franck and Hertz show the dependence of the electric current flowing out of the anode upon the electric potential between the grid and the cathode.

1. Rising curve in the current v/s accelerating plot corresponds to region where the electron gain kinetic energy due to excitation potential but not enough to ionize the medium (mercury).

2. Decaying curve corresponds to the region where the medium is ionized and hence energy is lost in ionisation.

3. Maxima corresponds to the point when the energy of the electrons is just enough to ionize the medium.

4. Minima corresponds to the point where electrons start to gain energy from the applied accelerating potential.

5. Ideally, the distance between two maxima is constant an equals the excitation potential of the medium. However, mercury has more than one excitation and ionization potential which makes the second and third peaks of the curve complicated.

6. The above observations suggest that the electrons give energy to the atoms in only discrete levels.

Rydberg formula:$λ1 =RZ_{2}(n_{′}_{2}1 −n_{2}1 )$ where Z=1 for hydrogen atom.

Now for sodium and mercury put $Z=11$ and $Z=80$ respectively and calculate the wavelength of the light used.

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