22.4 Photoelectric Effect 4.0

According to the conservation of energy principle, the kinetic energy of the ejected photoelectron is equal to the difference between the energy of the incident photon and the work required to free it from the metal surface (the work function).

 

Quantity	Symbol	SI Unit
kinetic energy	E k	J or eV
energy of the incident photon	E photon	J or eV
work function of the metal	W	J or eV

 

The energy of a charged particle in a uniform electric field is defined by

,

 

where q is the charge of an electron (1e ^- or 1.6 × 10 ^-19 C) and V _stop is the minimum voltage required to stop the photoelectric current.

 

The energy of a photon, according to Planck's formula is

,

 

where c is the speed of light, f is the frequency of the incident radiation and h is Planck's constant in either joules or electron volts.

 

h = 6.63 × 10 ^-34 J*s OR 4.14 × 10 ^-15 eV*s

 

The work function can be defined by the minimum frequency that can cause photoemission, which according to Planck's formula is , where f _o is the threshold frequency (minimum frequency of photon required to cause a photocurrent) and h is Planck's constant, in terms of joule seconds or electron volts seconds.

 

 

Example Problems

 

Problem 1.

What is the energy (in J and eV) of a photon of blue light that has a frequency of 6.67 × 10 ¹⁴ Hz?

 

Given

f = 6.67 × 10 ¹⁴ Hz

 

Required

the energy of the photon

 

Analysis and solution

 

Paraphrase

The energy is 4.42 × 10 ^-19 J or 2.76 eV.

 

 

 

Problem 2.

Light with a wavelength of 600 nm is directed at a metallic surface that has a work function of 1.60 eV.  What is the maximum kinetic energy (in J) of the emitted photoelectrons, their maximum speed, and the voltage needed to stop the photoelectric current?

 

Given

 

Required

the kinetic energy of the emitted photoelectrons, their maximum speed, and the voltage needed to stop the photoelectric current

 

Analysis and Solution

First convert the work function to joules.

 

 

Find the maximum kinetic energy.

 

 

To determine the speed of the photoelectrons, you must use the kinetic energy expressed in joules; eV won't work due to unit incompatibility!

 

 

To find the stopping voltage,

 

 

Paraphrase

The kinetic energy of the photoelectrons is 7.55 × 10 ^-20 J; their maximum speed is 4.07 × 10 ⁵ m/s; and the stopping voltage is 0.472 V.

      

Problem 3.

An electron is ejected from a metal with a speed of 4.7 × 10 ⁶ m/s.  The threshold frequency of the metal is 7.8 × 10 ¹⁴ Hz. What is the wavelength of the incident photon?

 

Given

 

Required

the wavelength of the incident photon

 

Analysis and Solution

 

Paraphrase

The wavelength of the photon is 1.9 × 10 ^-8 m or 19 nm.