A mercury lamp is a convenient souce for studying frequency dependence of photoelectric emission, since it gives a number of spectral lines ranging from the UV to the end of the red vissible spectrum. In our experiment with rubidium photocell, the following lines from a mercury source were used: `lambda_(1)=3650A^(@), lambda_(2)=4047A^(@), lambda_(3)=4358A^(@), lambda_(4)=5461A^(@), lambda_(5)=6907A^(@)` The stopping voltages, respectively were measured to be:
`V_(01)=1.28V, V_(02)=0.95V, V_(03)=0.74V, V_(04)=0.16V, V_(05)=0V`.
(a) Determine the value of Planck's constant h.
(b) Estimate the threshold frequency and work function for the material.

Explanation

(a) `v_(1)=c/(lambda_(1))=(3xx10^(8))/(3650xx10^(-10))=8.219xx10^(14)Hz, v_(2)=c/(lambda_(2))=(3xx10^(8))/(4040xx10^(-10))=7.412xx10^(14)Hz`,
`v_(3)=c/(lambda_(3))=(3xx10^(8))/(4358xx10^(-10))=6.884xx10^(14)Hz, v_(4)=c/(lambda_(4))=(3xx10^(8))/(5461xx10^(-10))=5.493xx10^(14)Hz`,
`v_(5)=c/(lambda_(5))=(3xx10^(8))/(6907xx10^(-10))=4.343xx10^(14)Hz` we know that, `eV_(0)=hv-phi_(0) or V_(0)=(hv)/e-(phi_(0))/e`
Hence a graph between frequency v and stopping potential `V_(0)`, must be a straght line. On plotting a graph between given frequencies v and corresponding values of stopping potential `V_(0)`, we get a straight line with first four points. This straight line is cutting v-axis at `5.0xx10^(14)Hz`. The fifth point comes in the range of `vltv_(0)`, which shows there is no photoelectric emission and hence no stopping is required to stope be current. From graph fig. The slope of this straight line,
`h/e=(V_(01)-V_(04))/(v_(1)-v_(4))=((1.28-0.16))/((8.219-5.493)xx10^(14))`
or `h=(1.12xx1.6xx10^(-19))/(2.726xx10^(14)) =6.574xx10^(-34)Js`
(b) Work function of metal, `phi_(0)=hv_(0)=6.574xx10^(-34)xx5xx10^(14)=32.870xx10^(-20)J=2.05eV`