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 . Determine the frequency (in hz) of the interacting photon.
frequency*wavelength=speed of light
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
To determine the frequency (in Hz) of the interacting photon, we can use the de Broglie wavelength formula and the relationship between frequency and wavelength.
The de Broglie wavelength (λ) of a particle can be determined using the following formula:
λ = h / p
Where:
λ is the de Broglie wavelength
h is the Planck's constant (6.626 × 10^-34 J·s)
p is the momentum of the particle
In this case, the de Broglie wavelength is given. Let's say the de Broglie wavelength is λ. Now, we need to relate the momentum (p) with the wavelength using the momentum-energy relationship for a photon.
The momentum of a photon can be calculated using the formula:
p = h / λ
Now, we can substitute the value of λ into the momentum formula:
p = h / λ
Next, we need to relate the momentum to the energy and the speed of light:
p = E / c
Where:
E is the energy of the photon
c is the speed of light (3 × 10^8 m/s)
Since we know the relationship between energy and frequency of a photon:
E = h * f
Where:
f is the frequency of the photon
We can substitute this expression for energy (E) into the momentum formula:
p = (h * f) / c
Now, equating the two expressions for momentum:
h / λ = (h * f) / c
We can solve this equation for frequency (f):
f = c / λ
Now, we can substitute the given value of the de Broglie wavelength (λ) into this equation to find the frequency (f) of the interacting photon:
f = c / λ