Early photoelectric light detectors were based on cesium. Cesium metal has a work function of 3.43 *10^-¹⁹ J. What is the kinetic energy of the photoelectrons ejected from a cesium surface when exposed to blue light at 400 nm? A) 5.41*10^-¹⁸ J B) 5.14 *10^-²⁰ J C) 2.54*10^-¹⁷ J D) 1.54 *10^-¹⁹ J E) 2.54 * 10^-¹⁹ J

Question

Quizplus · Accepted Answer

The formula for calculating the kinetic energy of photoelectrons is:
K.E. = hν - Φ
where h is Planck's constant, ν is the frequency of light, and Φ is the work function of the metal.

First, we need to find the frequency of blue light at 400 nm using the formula:
c = λν
where c is the speed of light and λ is the wavelength of light.

c = 3.00 x 10^8 m/s
λ = 400 nm = 4.00 x 10^-7 m

ν = c/λ = (3.00 x 10^8 m/s)/(4.00 x 10^-7 m) = 7.50 x 10^14 Hz

Now we can calculate the kinetic energy of the photoelectrons:
K.E. = hν - Φ = (6.63 x 10^-34 J s)(7.50 x 10^14 Hz) - 3.43 eV*(1.60 x 10^-19 J/eV)
K.E. = 1.54 x 10^-19 J

Converting to electron volts:
K.E. = (1.54 x 10^-19 J)/(1.60 x 10^-19 J/eV) = 0.963 eV

Therefore, the answer is D) 1.54 x 10^-19 J or 0.963 eV.

Early Photoelectric Light Detectors Were Based on Cesium