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
Question
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
Solution
a) The minimum energy needed to remove an electron from the metal surface, also known as the work function (Φ), can be calculated using the equation of the photoelectric effect:
E = Φ + KE
where E is the energy of the incoming photon, Φ is the work function, and KE is the kinetic energy of the emitted electron.
The energy of the incoming photon can be calculated using the equation:
E = hc/λ
where h is Planck's constant (6.626 x 10^-34 Js), c is the speed of light (3.00 x 10^8 m/s), and λ is the wavelength of the light (300 nm = 300 x 10^-9 m).
E = (6.626 x 10^-34 Js)(3.00 x 10^8 m/s) / (300 x 10^-9 m) = 6.626 x 10^-19 J
The kinetic energy of the emitted electron is given as 1.68 x 10^5 J/mol. To convert this to energy per electron, we divide by Avogadro's number (6.022 x 10^23 mol^-1):
KE = 1.68 x 10^5 J/mol / 6.022 x 10^23 mol^-1 = 2.79 x 10^-19 J
Now we can calculate the work function:
Φ = E - KE = 6.626 x 10^-19 J - 2.79 x 10^-19 J = 3.836 x 10^-19 J
b) The maximum wavelength that will cause the photoelectric effect is the wavelength that corresponds to the work function. We can calculate this using the equation:
λ = hc/Φ
λ = (6.626 x 10^-34 Js)(3.00 x 10^8 m/s) / 3.836 x 10^-19 J = 518 nm
So, the maximum wavelength that will cause the photoelectric effect is 518 nm.
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