Question

It takes 261 kJ/mol to eject electrons from a certain metal surface. What is the longest wavelength of light (nm) that can be used to eject electrons from the surface of this metal via the photoelectric effect?

Answer 1

Answer: 459 nm

Step-by-step explanation:

The relation between energy and wavelength of light is given by Planck's equation, which is:

`E=(Nhc)/(\lambda)`

where,

E = energy of the light =
`261 kJ=261000J` (1kJ=1000J)

N= avogadro's number =
`6.023* 10^(23)`

h = Planck's constant =
`6.626* 10^(-34)Js`

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

`\lambda` = wavelength of light = ?

Putting the values in the equation:

`261000J=(6.023* 10^(23)* 6.626* 10^(-34)Js* 3* 10^8m/s)/(\lambda)`

`\lambda=4.587* 10^(-7)m=459nm`
`1nm=10^(-9)m`

Thus the longest wavelength of light that can be used to eject electrons from the surface of this metal via the photoelectric effect is 459 nm