The work function energy of potassium is 2.2 eV.
The surface of potassium is illuminated with electromagnetic radiation of a specific wavelength.
Experiments show that the photoelectrons from potassium have kinetic energy in the range zero to 1.9 eV.
Determine the wavelength of the incident electromagnetic radiation.
work function= 2.2-1.9 ev
remember E=hc/lambda
energy work funciton= .3 ev= .3*(1Joule / 6.24•1018eV)
so lambda= speedlight/energyWorkFuncionInJoules
To determine the wavelength of the incident electromagnetic radiation, we can use the equation:
E = hf - Φ
Where:
E is the kinetic energy of the photoelectrons
h is Planck's constant (6.626 x 10^-34 J.s or 4.136 x 10^-15 eV.s)
f is the frequency of the incident radiation
Φ is the work function energy
Given:
Φ = 2.2 eV
E = 1.9 eV
We need to convert the energies to joules by multiplying by the conversion factor (1 eV = 1.6 x 10^-19 J).
Φ = 2.2 eV * 1.6 x 10^-19 J/eV = 3.52 x 10^-19 J
E = 1.9 eV * 1.6 x 10^-19 J/eV = 3.04 x 10^-19 J
Now, we rearrange the equation to solve for the frequency:
f = (E + Φ) / h
f = (3.04 x 10^-19 J + 3.52 x 10^-19 J) / (6.626 x 10^-34 J.s)
f = 6.56 x 10^14 Hz
Finally, we can calculate the wavelength using the formula:
λ = c / f
Where:
c is the speed of light (3 x 10^8 m/s)
λ = (3 x 10^8 m/s) / (6.56 x 10^14 Hz)
λ ≈ 457 nm
Therefore, the wavelength of the incident electromagnetic radiation is approximately 457 nm.
To determine the wavelength of the incident electromagnetic radiation, we can use the relationship between the kinetic energy of the photoelectrons and the energy of the incident photons.
1. Convert the energy values from electron volts (eV) to joules (J):
- The work function energy of potassium, 2.2 eV, can be converted to joules by multiplying it by the conversion factor 1.602 x 10^-19 J/eV.
So, 2.2 eV * 1.602 x 10^-19 J/eV = 3.524 x 10^-19 J.
- The maximum kinetic energy of the photoelectrons is given as 1.9 eV, which can be converted to joules using the same conversion factor.
So, 1.9 eV * 1.602 x 10^-19 J/eV = 3.0458 x 10^-19 J.
2. Next, we can use the equation relating the energy of a photon (E) to its wavelength (λ) in meters:
E = h * c / λ,
where h is the Planck's constant (6.626 x 10^-34 J·s) and c is the speed of light (3 x 10^8 m/s).
3. Rearranging the equation, we get:
λ = h * c / E.
4. Substitute the values into the equation:
λ = (6.626 x 10^-34 J·s * 3 x 10^8 m/s) / 3.0458 x 10^-19 J.
5. Calculate the wavelength:
λ = 6.874 x 10^-7 m.
Therefore, the wavelength of the incident electromagnetic radiation is approximately 687.4 nm (nanometers).