A mercury lamp is a convenient source for studying frequency dependence of photoelectric emission, since it gives a number of spectral lines ranging from the Uv to the red end of the visible spectrum. In our experiment with rubidium photo-cell, the following lines from a mercury source were used:
`lambda_(1) = 3650 Å, lambda_(2) = 4047 Å, lambda_(3) = 4358 Å, lambda_(4) = 5461 Å, lambda_(5) = 6907 Å`,
The stopping voltages, respectively, were measured to be:
`V_(01) = 1.28 V, V_(02) = 0.95 V, V_(03) = 0.74 V, V_(04) = 0.16 V, V_(05) = 0 V`
Determine the value of Planck’s constant h, the threshold frequency and work function for the material.
[Note: You will notice that to get h from the data, you will need to know e (which you can take to be `1.6 xx 10^(-19) C`). Experiments of this kind on Na, Li, K, etc. were performed by Millikan, who, using his own value of e (from the oil-drop experiment) confirmed Einstein’s photoelectric equation and at the same time gave an independent estimate of the value of h.]

Explanation

(a)From frequency `v=(c )/(lambda)`,
`V_(1)=(c )/(lambda_(1))=(3xx10^(8))/(3650xx10^(-10))=8.219xx10^(14)Hz`
`V_(2)=(c )/(lambda_(2))=(3xx10^(8))/(4047xx10^(-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
`therefore`

Slope of graph=`(BC)/(AC)`
`(DeltaV_(0))/(DeltaV)=(1.28-0)/((8.2-5.0)xx10^(14))`
`=(1.28)/(302xx10^(14))=0.4xx10^(-14)`
`=4xx10^(-15)`Vs
`implies`From Einstein.s photoelectric equation,
`eV_(0)=hV-phi_(0)`
`therefore eDeltaV_(0)=hDeltaV[because phi_(0)=constant]`
`therefore (DeltaV_(0))/(DeltaV)=(h)/(e)`
`therefore h=exx(DeltaV_(0))/(Deltav)`
`=1.6xx10^(-19)xx4.0xx10^(-15)`
`=6.4xx10^(-34)Js`
(b)Threshold frequency,
`V_(0)=5.0xx10^(14)`Hz
Which is obtained from `V_(0)tov` graph.
Work function.
`phi_(0)=hv_(0)`
`=6.63xx10^(-34)xx5xx10^(14)`
`=33.15xx10^(-20)J`