1.

When an atom X absorbs radiation with a photon energy than the ionization energy of the atom, the atom is ionized to generate an ion X^(+) and the electron (called a photoelectron) is ejected at the same time. In this event, the energy is conserved as shown in Figure 1, that is, Photon energy (h)=ionization energy (IE) of X+ kinetic energy of photoelectron. When a molecule, for example, H_(2), absorbs short-wavelength light, the photoelectron is ejected and an H_(2), ion with a variety of vibrational states is produced. A photoelectron spectrum is a plot of the number of photoelectrons as a function of the kinetic energy of the photoelectrons. Figure-2 shows a typical photoelectron spectrum when H_(2) in the lowest vibrational level is irradiated by monochromatic light of 21.2 eV. No photoelectrons are detected above 6.0 eV. (eV is a unit of energy and 1.0 eV is equal to 1.6xx10^(-19) J) Figure 1 Schematic diagram of photoelectron spectroscopy. Figure 2 Photoelectron spectrum of H_(2). The energy of the incident light is 21.2 eV ul("Calculate") the ionization energy E_(B)( eV) of the hydrogen atom to the first decimal place. The energy threshold for the generation of two electronically excited hydrogen atoms H^(**) (n=2) from H_(2)(v=0) has been derived to be 24.9 eV by an experiment.

Answer»


Answer :The ionization energy corresponds to `n=oo`. Accordingly,
`DeltaE_(n=2larr n=1)=`^(3)//_(4) RY``
`DeltaE_(n=2 larr n=1)=Ry`
Thus, the energy required for the ionization is `4/3` TIMES larger than the TRANSITION energy of the Lyman `alpha`-LINE.
`E_(B)=10.2 eVxx4/3=13.6 eV`


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