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CBSE Class 12-science Answered

For radiation of wavelength lambda,the stoping potential is 3v0 and for 2 lambda, the stoping potential is v0.find the threshhold wavelength 
Asked by Parasbir99 | 11 Nov, 2018, 07:02: AM
answered-by-expert Expert Answer
Einstein's photoelectric equation :-  begin mathsize 12px style h nu space equals space w space plus space 1 half m v squared space space.................. left parenthesis 1 right parenthesis end style
where ν is the frequency of incident electro-magnetic radiation, w is the workfuction in energy units and
this workfunction is the characterstic of photoelectric material. 
 
Second term of LHS of eqn.(1) is the kinetci energy of ejected electron.
Eqn.(1) can be rewritten in terms of wavelength of incident radiation and by replacing the workfunction as
the equivalent threshold wavelength λth . Kinetic energy also can be replaced by stopping potential V.
 
Hence the modified equation is, begin mathsize 12px style fraction numerator h c over denominator lambda end fraction space equals space fraction numerator h c over denominator lambda subscript t h end subscript end fraction space plus space e V space...................... left parenthesis 2 right parenthesis end style
if we substitute the given data in eqn.(2), we get the following equations.

begin mathsize 12px style fraction numerator h c over denominator lambda end fraction space equals space fraction numerator h c over denominator lambda subscript t h end subscript end fraction space plus space e space 3 v subscript 0 space................... left parenthesis 3 right parenthesis fraction numerator begin display style h c end style over denominator begin display style 2 lambda end style end fraction space equals space fraction numerator begin display style h c end style over denominator begin display style lambda subscript t h end subscript end style end fraction space plus space e space v subscript 0 space...................... left parenthesis 4 right parenthesis end style
By solving eqns.(3) and (4) for λth ,  we get λth = 4λ
 
Answered by Thiyagarajan K | 11 Nov, 2018, 09:25: AM

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