Quick question on calculating wavelength.

[lyrebird]

Homework Statement

Light strikes a sodium surface, causing photoelectric emission. The stopping potential for the ejected electrons is 4.6 V, and the work function of sodium is 2.2 eV. What is the wavelength of the incident light?

Homework Equations

The Attempt at a Solution

Problem solved, thanks. :)

 

[Stonebridge]

The equation E=hf for the energy of a photon of frequency f, will give energy in joules. (if h is in SI units)
So the work function and maximum ke of electrons (given by the stopping potential) also need to be in joules.

 

[lyrebird]

The equation E=hf for the energy of a photon of frequency f, will give energy in joules. (if h is in SI units)
So the work function and maximum ke of electrons (given by the stopping potential) also need to be in joules.

To calculate the maximum kinetic energy, I would just multiply the charge on an electron by the stopping potential 4.6V, wouldn't I?

 

[Stonebridge]

To calculate the maximum kinetic energy, I would just multiply the charge on an electron by the stopping potential 4.6V, wouldn't I?

Yes. That's correct. It's the same idea as calculating the k.e. an electron gains when accelerating through a potential V. The only difference here is that the electric field acts to decelerate the electron rather than accelerate it.

 

[paranormal]

I would like to provide a more detailed response to this question. The wavelength of the incident light can be calculated using the equation:

λ = hc/Φ

Where λ is the wavelength, h is Planck's constant, c is the speed of light, and Φ is the work function. Plugging in the values given in the problem, we get:

λ = (6.626 x 10^-34 J s)(3.00 x 10^8 m/s)/(2.2 eV x 1.602 x 10^-19 J/eV)

λ = 3.61 x 10^-7 m or 361 nm

This means that the incident light has a wavelength of 361 nanometers. This calculation is based on the photoelectric effect, which is the emission of electrons from a material when it is exposed to light of a certain frequency or wavelength. The stopping potential of 4.6 V refers to the minimum energy required to stop the emission of electrons from the sodium surface, which is equal to the work function of 2.2 eV. By using the equation above, we can determine the wavelength of the incident light that caused this emission.