Question

1. In an experiment similar to that carried out by Philipp Lenard in 1902, a sodium metal plate is first illuminated with light of wavelength λ1 = 420 nm, which gives a measured stopping potential of −0.65 V. Then, the light’s wavelength is set to λ2 = 310 nm and the measured stopping potential is −1.69 V.

(a) From these measurements, calculate a value of Planck’s constant h multiplied by c (the speed of light) in units of eV nm. Is your result consistent within an accuracy of ±1% of the standard value of hc = 1240 eV nm ?

(b) From these measurements, calculate the work function of the sodium plate.

(c) In a similar experiment, the wavelength of light is fixed at 420 nm, but the light source has a higher power. It is observed that the rate at which electrons are ejected from the same plate is larger than from the lower power light source (at wavelength 420 nm). Describe how Einstein’s model of photons provides an explanation for this result.

(d) For another experiment which has the same power for its light source as part (c), but the light is at a wavelength of 300 nm, the rate at which electrons are ejected from the same plate is lower than part (c). Describe how Einstein’s model of photons explains this.

Answer 1

1] Stopping potential is the reverse potential difference applied for which the photocurrent is made zero. Therefore, the kinetic energy of the ejected electrons = qV

=>

substitute the values to get: hc = 1230.982 eVnm

b] Use this value in the 1st expression to get:

c] Increasing the power of the light source while keeping the same wavelength means that more photons of the same energy are now hitting the target. So while the kinetic energy of the ejected electrons remains the same, the number of ejected electrons increase thereby increasing the rate of ejection. This means that the stopping potential for the increased power case must remain the same. This is consistent with Einstein's model of photoelectric effect which says that the intensity is inconsequential to the kinetic energy of the ejected electrons.

d] Now, with the same power, the wavelength is reduced so all the photons now have more energy in them. This means that the kinetic energy per electron increases thereby changing the required stopping potential. Here, the rate of ejection is thus lower than in [c] which is again consistent with Einstein's model of photoelectric effect.