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 0.468×10−10 m. Determine the frequency (in hz) of the interacting photon.

frequency(wavelength)=speed of light.

solve for frquency.

1.67E17

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

1.71*10^17

Right answer

To determine the frequency of the interacting photon, we need to use the wavelength of the ejected electron and the de Broglie relation.

The de Broglie relation states that the wavelength (λ) of a particle is related to its momentum (p) by the equation:
λ = h / p

Where:
λ is the wavelength of the particle
h is the Planck constant (6.626 × 10^-34 J·s)
p is the momentum of the particle

In this case, the ejected electron is the particle, and its momentum can be related to the photon's momentum. Since the photon is absorbed, its momentum is transferred to the electron.

Using the conservation of momentum:
p_photon = p_electron

The momentum of a photon is given by:
p_photon = h / λ_photon

And the momentum of an electron can be calculated using its mass (m) and velocity (v):
p_electron = m_electron * v_electron

Now, since the electron is ejected from the hydrogen atom, it gains kinetic energy equal to the energy of the absorbed photon. The energy of a photon (E_photon) can be related to its frequency (f) using the equation:
E_photon = h * f

Using the energy conservation equation:
E_photon = E_kinetic_electron

E_kinetic_electron can be calculated using the equation:
E_kinetic_electron = 0.5 * m_electron * v_electron^2

Now, we can equate the energy equations and the momentum equations to find the frequency of the interacting photon.

E_photon = E_kinetic_electron
h * f = 0.5 * m_electron * v_electron^2

We can substitute the momentum equations into the energy equation:

h * f = 0.5 * m_electron * (p_electron / m_electron)^2

Simplifying the equation gives:

f = (p_electron^2) / (2 * h * m_electron)

Now we can substitute the de Broglie wavelength equation into the frequency equation:

f = (h / λ_electron^2) / (2 * h * m_electron)

Finally, we can plug in the given values to calculate the frequency:

λ_electron = 0.468 × 10^-10 m
m_electron = 9.10938356 × 10^-31 kg
h = 6.626 × 10^-34 J·s

f = (6.626 × 10^-34 J·s / (0.468 × 10^-10 m)^2) / (2 * (6.626 × 10^-34 J·s) * (9.10938356 × 10^-31 kg))

Calculating this expression will give you the frequency of the interacting photon in Hz.