Question

The following table lists the work functions of a few commonmetals, measured in electron volts.

Metal \Phi\,({\rm eV})
Cesium 1.9
Potassium 2.2
Sodium 2.3
Lithium 2.5
Calcium 3.2
Copper 4.5
Silver 4.7
Platinum 5.6
Using these data, answer the following questions about thephotoelectric effect.


Part A
Light with a wavelength of 190 \rm nm is incident on a metal surface. Themost energetic electrons emitted from the surface are measured tohave 4.0 \rm eV of kinetic energy. Which of the metalsin the table is the surface most likely to be made of?


cesium
potassium
sodium
lithium
calcium
copper
silver
platinum

Answer 1

Lithium

Step-by-step explanation:

The equation for the photoelectric effect is

`(hc)/(\lambda)= \phi + K_(max)`

where

`(hc)/(\lambda)` is the energy of the incident photon, with

h being the Planck constant

c is the speed of light

`\lambda` is the wavelength of the photon

`\phi` is the work function of the metal (the minimum energy needed to extract the photoelectron from the metal)

`K_(max)` is the maximum kinetic energy of the emitted photoelectrons

In this problem, we have

`\lambda= 190 nm = 1.9\cdot 10^(-7)m` is the wavelength of the incident photon

`K_(max)=4.0 eV` is the maximum kinetic energy of the electrons

First of all we can find the energy of the incident photon

`E=((6.63\cdot 10^(-34) Js)(3\cdot 10^8 m/s))/(1.90\cdot 10^(-7) m)=1.05\cdot 10^(-18) J`

Converting into electronvolts,

`E=(1.05\cdot 10^(-18) J)/(1.6\cdot 10^(-19) J/eV)=6.6 eV`

So now we can re-arrange the equation of the photoelectric effect to find the work function of the metal

`\phi = E-K_(max)=6.6 eV - 4.0 eV=2.6 eV`

So the metal is most likely Lithium, which has a work function of 2.5 eV.