The minimum wavelength of paschen series of hydrogen atom will be For Paschen Series, n=3, and mimimum wavelength occurs when transition occurs just from series limit, λhC=−13.6[n121−n221] ⇒λ=13.6×[91−1]−4.14×10−15×3×108 ⇒λ=13.6×84.14×10−15×3×108×9 ⇒λ=1.878655×10−6×9×0.04861111 m ⇒λ=8.21911×10−07m ⇒λ=8219.11×10−10 m ⇒λ=8219A∘≈8181A∘
Franck and Herts Experiment
Franck and Hertz's original experiment used a heated vacuum tube containing a drop of mercury; they reported a tube temperature of 1150 C, at which the vapor pressure of mercury is about 100 pascals (and far below atmospheric pressure). It is fitted with three electrodes: an electron-emitting, hot cathode; a metal mesh grid; and an anode. The grid's voltage is positive relative to the cathode, so that electrons emitted from the hot cathode are drawn to it. The electric current measured in the experiment is due to electrons that pass through the grid and reach the anode. The anode's electric potential is slightly negative relative to the grid, so that electrons that reach the anode have at least a corresponding amount of kinetic energy after passing the grid. 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.
Conclusions from the plot of Franck and Hertz experiment
Some conclusions that can be drawn from the graph plotted in the Franck and Hertz experiment are as follows: 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.
Wavelength of a spectral line emitted by mercury and sodium lamps
The emission spectrum of atomic hydrogen is divided into a number of spectral series, with wavelengths given by the Rydberg formula. These observed spectral lines are due to the electron making transitions between two energy levels in the atom. Rydberg formula:λ1=RZ2(n′21−n21) 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.