A photon interacts with a ground state electron in a hydrogen atom and is absorbed. The electron is ejected from the atom and exhibits a de Broglie wavelength of 3.188×10−10 m. Determine the frequency (in hz) of the interacting photon.
frequency * wavelength=speed light
no
the wavelength is for electron, whereas the frequency of photon is needed
First find: E = P^2/2Me + E(first ionization)
P= h / BroglieWavelength
E(first ionization)=21.7*10^-19
Me= 9.1*10^-31
h= 6.626*10^-34
Once E is found the find frequency:
frequency(hz)= E / h
thanks!
To determine the frequency of the interacting photon, we will use the de Broglie wavelength formula and the energy equation for a photon.
1. De Broglie Wavelength Formula:
The de Broglie wavelength (λ) of a particle is given by the equation:
λ = h / p
where λ is the de Broglie wavelength, h is the Planck's constant (6.626 × 10^-34 J·s), and p is the momentum of the particle.
2. Energy of a Photon:
The energy (E) of a photon is related to its frequency (ν) by the equation:
E = h · ν
where E is the energy of the photon, h is the Planck's constant, and ν is the frequency of the photon.
Now, let's solve the problem step by step:
Step 1: Calculate the momentum of the ejected electron.
Since the de Broglie wavelength (λ) is given as 3.188×10^(-10) m, we can find the momentum (p) using the de Broglie wavelength formula:
p = h / λ
Substituting the values:
p = (6.626 × 10^-34 J·s) / (3.188×10^(-10) m)
Step 2: Calculate the energy of the photon.
Since the electron is ejected, the energy of the photon is equal to the total energy required to remove the electron from the atom. This energy is given by the equation:
E = E_initial - E_final
In this case, the initial energy (E_initial) is the energy of the ground state electron, which is equal to the ground state energy of a hydrogen atom (E_initial = -13.6 eV).
The final energy (E_final) is 0 eV because the electron is ejected from the atom.
Converting -13.6 eV to joules (since energy is usually measured in J):
E_initial = -13.6 eV x (1.6 × 10^-19 J/eV)
Step 3: Calculate the frequency of the photon.
Using the energy equation for a photon:
E = h · ν
Substitute the calculated values for the energy (E) and solve for the frequency (ν):
ν = E / h
Substituting the values and converting E_initial to Joules:
ν = (-13.6 x 1.6 × 10^-19 J) / (6.626 × 10^-34 J·s)
Now, perform the calculations to find the frequency (ν) in Hz.