The binding energy of an electron to a metal surface is 184 kJ/mol. What is the threshold wavelength (in nm) for the onset of the photoelextric effect?
From the binding energy per mole, convert that to binding energy per electron (divide by avagradros number).
Then, E=h*c/lambda and solve for lambda
Convert 184 kJ/mol to J/atom.
184,000 x (1 mol/6.02 x 10^23 atoms) = ??J/atom.
Now delta E = hc/lambda.
You have delta E from the first calculation, you know h from one of your earlier problems, c is the speed of light in m/s; therefore, calculate lambda in meters. Then change meters to nm.
Post your work if you get stuck.
To determine the threshold wavelength for the onset of the photoelectric effect, we need to use the equation:
1/λ = R(1/n₁² - 1/n₂²),
where λ is the wavelength, R is the Rydberg constant (1.0973731568508 × 10^7 m⁻¹), n₁ is the principal quantum number of the lower energy level (initial state), and n₂ is the principal quantum number of the higher energy level (final state).
In this case, the photoelectric effect involves the electron being ejected from the metal surface, so n₁ would be the energy level of the bound electron, and n₂ would be the energy level of the ejected electron (which approaches infinity). Since the electron is bound to the metal surface, n₁ would typically be considered as 1.
To convert the binding energy (BE) given in kJ/mol to energy per photon (E), we use the Avogadro's constant (6.022 × 10^23 mol⁻¹):
E = BE / N,
where N is the Avogadro's constant.
Now, to convert the energy of a single photon (E) into its corresponding wavelength (λ), we can use the equation:
E = hc / λ,
where h is the Planck's constant (6.62607015 × 10⁻³⁴ J·s) and c is the speed of light (2.998 × 10⁸ m/s).
Let's calculate the threshold wavelength step by step:
1. Convert the binding energy to energy per photon:
BE = 184 kJ/mol,
N = 6.022 × 10^23 mol⁻¹.
E = BE / N,
E = 184 × 10³ J/mol / (6.022 × 10^23 mol⁻¹).
2. Convert the energy of a single photon to wavelength:
E = hc / λ,
λ = hc / E,
λ = (6.62607015 × 10⁻³⁴ J·s) × (2.998 × 10⁸ m/s) / E.
Now substitute the value of E from step 1 into the equation above and convert the result to nanometers (nm).
This will give you the threshold wavelength (in nm) for the onset of the photoelectric effect.