Question

The maximum wavelength that an electromagnetic wave can have and still eject electrons from a metal surface is 459 nm. What is the work function W0 of this metal? Express your answer in electron volts.

Answer 1

2.7067 eV

Step-by-step explanation:

h = Planck's constant =
`6.626* 10^(-34)\ m^2kg/s`

c = Speed of light =
`3* 10^8\ m/s`

`\lambda_0` = Threshold wavelength = 459 nm

Work function is given by

`W_0=(hc)/(\lambda_0)\\\Rightarrow W_0=(6.626* 10^(-34)* 3* 10^8)/(459* 10^(-9))\\\Rightarrow W_0=4.33072* 10^(-19)\ J`

Converting to eV

`1\ J=(1)/(1.6* 10^(-19))\ eV`

`4.33072* 10^(-19)\ J=4.33072* 10^(-19)* (1)/(1.6* 10^(-19))\ eV=2.7067\ eV`

The work function W0 of this metal is 2.7067 eV