The equation for the photoelectric effect is
#color(blue)(bar(ul(|color(white)(a/a)hf = Φ + KEcolor(white)(a/a)|)))" "#
where
#h color(white)(ml)= # Planck's constant
#f color(white)(ml)= # the frequency of the incident light
#Phicolor(white)(m) =# the work function
#KE =# the kinetic energy of the ejected electron
We can rearrange the equation to get
#KE = hf - Phi#
Compare this equation with that for a straight line.
#KE = hf - Phi#
#color(white)(ll)ycolor(white)(ll) = mx + b#
Thus, a plot of #KE# vs #f# is a straight line with slope #h"# and #x#- intercept #Phi#.
I converted the wavelengths to frequencies and got the following dataset.
The plot of #KE# vs #f# looked like this.
The calculated equation for the line is #KE = "0.004 118"f- 2.240#
The #y#-intercept is at
#"0 = "0.004 118"f- 2.2404#
#f = 2.2404/"0.004 118" = "544 THz"#
#"slope" = h =("0.004 118" color(red)(cancel(color(black)("eV"))))/(1 color(red)(cancel(color(black)("THz")))) ×(1.602 × 10^"-19" color(white)(l)"J")/(1 color(red)(cancel(color(black)("eV")))) × (1 color(red)(cancel(color(black)("THz"))))/(10^12color(white)(l) "s"^"-1") =#
#6.597 × 10^"-34"color(white)(l) "J·s"#
The experimental value for #h = 6.597 × 10^"-34"color(white)(l) "J·s"#.
The work function corresponds to the point where the excess kinetic energy of the electron is zero.
#0 = hf - Phi#
#Phi = hf = 6.626 × 10^"-34"color(white)(l) "J·"color(red)(cancel(color(black)("s"))) × 544 × 10^12 color(red)(cancel(color(black)("s"^"-1"))) = 3.60 × 10^"-19"color(white)(l) "J"#
In electron volts, the work function is
#Phi = 3.60 × 10^"-19" color(red)(cancel(color(black)("J"))) × "1 eV"/(1.602 × 10^"-19" color(red)(cancel(color(black)("J")))) = "2.25 eV"#
