Light consisting of two wavelengths, ?a = 4.6 x 10-7 meter and ?b = 6.3 x 10-7 m

Question

Light consisting of two wavelengths, ?a = 4.6 x 10-7 meter and ?b = 6.3 x 10-7 meter, is incident normally on a barrier with two slits separated by a distance d. The intensity distribution is measured along a plane that is a distance L = 0.84 meter from the slits as shown above. The movable detector contains a photoelectric cell whose position y is measured from the central maximum. The first order maximum for the longer wavelength ?b occurs at y = 2.0 x 10-2 meter.

(a) Determine the slit separation d. _________ m

(b)At what position yadoes the first order maximum occur for the shorter wavelength ?a? _______ m

In a different experiment, light containing many wavelengths is incident on the slits. It is found that the photosensitive surface in the detector is insensitive to light with wavelengths longer than5.4x 10-7m.

(c) Determine the work function of the photosensitive surface. _______ eV

(d)Determine the maximum kinetic energy of electrons ejected from the photosensitive surface when exposed to light of wavelength ? =4.6x 10-7m. _______ eV

Explanation / Answer

1 = 4.6 * 10-7 m

2= 6.3*10^(-7)m

L=0.84m

a) y = 2L/d

d = 2L/y = 6.3 *10^(-7)*0.84/(2*10^-2) = 2.646*10-5

b) y = 1L/d = 1.4*10^-2 m

c) Work function (W) = hc/ = 3.68 * 10^(-19) J = 2.3 eV

d) KE = hc/(4.6*10-7 ) - W = 0.64 * 10^(-19) J= 0.4 eV

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