When light shines on a metal surface, it can cause electrons to be emitted through the photoelectric effect. In this case, the speed of the ejected electron can be found using the energy equation and the given wavelength of light. The speed of the ejected electron is approximately 1.92 x 10^6 m/s.
Step-by-step explanation:
When light shines on a metal surface, it can cause electrons to be emitted through the photoelectric effect. In order for this to happen, the energy of the photons must be greater than the work function of the metal. The work function is the minimum amount of energy needed to remove an electron from the metal surface.
In this case, the wavelength of the light is given as 285 nm. To find the speed of the ejected electron, we can use the energy equation:
Energy of photon = Energy to remove electron
Using the equation E = hc/λ, where E is the energy in joules, h is Planck's constant (6.626 x 10^-34 J*s), c is the speed of light (3.0 x 10^8 m/s), and λ is the wavelength in meters, we can find the energy of the photon.
Then, we can equate this energy to the work function and solve for the speed of the ejected electron using the equation:
Energy of electron = (1/2)mv^2, where m is the mass of the electron (9.11 x 10^-31 kg) and v is its speed in m/s.
Plugging in the values and solving the equations, we find that the speed of the ejected electron is approximately 1.92 x 10^6 m/s.