When wave B shines on a metal surface, it just barely fails to eject an electron to cause a current (photoelectric effect):... What is the wavelength of B (in nm), if the energy required to eject a photoelectron is 213 kJ/mol
Question
When wave B shines on a metal surface, it just barely fails to eject an electron to cause a current (photoelectric effect):... What is the wavelength of B (in nm), if the energy required to eject a photoelectron is 213 kJ/mol
Solution
To solve this problem, we need to use the equation for the energy of a photon, which is E = hc/λ, where E is the energy of the photon, h is Planck's constant, c is the speed of light, and λ is the wavelength of the light.
-
First, we need to convert the energy from kJ/mol to J/photon. We know that 1 mol of photons contains Avogadro's number (6.022 x 10^23) of photons. So, 213 kJ/mol is equivalent to 213 x 10^3 J/mol. Dividing this by Avogadro's number gives us the energy per photon in Joules.
E = (213 x 10^3 J/mol) / (6.022 x 10^23 photons/mol) = 3.54 x 10^-19 J/photon
-
Next, we can use this energy to find the wavelength of the light. Rearranging the equation for the energy of a photon gives us λ = hc/E.
Planck's constant h = 6.626 x 10^-34 J*s Speed of light c = 3.00 x 10^8 m/s Energy E = 3.54 x 10^-19 J/photon
λ = (6.626 x 10^-34 J*s * 3.00 x 10^8 m/s) / 3.54 x 10^-19 J/photon = 5.63 x 10^-7 m
-
Finally, we need to convert this wavelength from meters to nanometers. 1 m = 10^9 nm, so:
λ = 5.63 x 10^-7 m * 10^9 nm/m = 563 nm
So, the wavelength of wave B is approximately 563 nm.
Similar Questions
When sodium metal surface is exposed to radiation of 300 nm, electrons with kinetic energy KE= 1.68 x 105 Jmol-1 are emitted.a) Calculate the minimum energy needed to remove an electron from the metal surface.b) What is the maximum wavelength that will cause photoelectric effect
Light of wavelength 390 nm is directed at a metal electrode. To find the energy of electrons ejected, an opposing potential difference is established between it and another electrode. The current of photoelectrons from one to the other is stopped completely when the potential difference is 1.10 V. Determine i) the work function of the metal and ii) the maximum wavelength of light that can eject electrons from this metal. (amplify the signal?)
The work function of a metal is 31 eV. To eject a photoelectron of zero velocity from the surface of the metal the wavelength of incident light should be above
Light of wavelength 180nm strikes a metal target and photoelectrons are emitted. It is noticed that the photocurrent drops to zero at stopping potential of 0.8 V. The work function of the metal surface is___________a.None of theseb.5.03 eVc.6.09 eVd.3 eVe.3.7 eV
Light of wavelength 200 nm falls on an aluminum surface, having workfunction 4.2 eV. What is the K.E. of the fastest emitted photoelectron? Alsofind the stopping potential and cutoff wavelength.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.