An X-ray pulse of wavelength 4.9Å is sent through a section of Wilson cloud chamber containing a super saturated gas, and tracks of photoelectrons ejected from the gaseous atom are observed. Two groups of tracks of length 1.40cm and 2.02 cm are noted. If the range-energy relation for cloud chamber is given by `R=alphaE`, with `alpha=1cm//keV`, obtain the binding energies of two levels from which electrons are emitted. Given `h=6.63xx10^(-34)Js , e=1.6xx10^(-19)C`.

Explanation

Here, `lambda=4.9xx10^(-10)m , R_(1)=1.4cm`,
`R_(2)=2.02cm , alpha=1cm//keV`.
For cloud-chamber, the range-energy relation is
`R=alphaE or E=R/alpha`
`:. E_(1)=(R_(1))/alpha=(1.40cm)/(1cm//keV)=1.40keV`
`E_(2)=(R_(2))/alpha=(2.02cm)/(1cm//keV)=2.02keV`
Energy of the incident photon
`E=(hc)/lambda=((6.63xx10^(-34))xx(3xx10^(8)))/(4.9xx10^(-10))J`
`=(6.63xx3xx10^(-16))/(4.9xx1.6xx10^(-16))keV=2.54keV`
From Einstein's photoelectric equation
`(hc)/lambda=phi+E`
Binding energy, `phi=(hc)/lambda-E`
or `phi_(1)=2.54-1.40=1.14keV`
and `phi_(2)=2.54-2.02=0.52keV`