Calculate the energy of photon in ev emitted by an electron

Question

Question:

Show that the emission of hydrogen atom from n=6 to n=2 does have a wavelength of 410 nm.

Given that the energy of hydrogen-like atom is written as: (all of them are equivalent)

Part 1 - Familiarize with equations

Write down the equation of: Example: Energy Single Electron Atom

E_n = -13.6eV (z²/n²)

1. Energy Multi Electron Atom.

2. Energy Particle in a Box.

3. Photoelectric Effect (wavelength, work function, and speed of e^-).

4. Energy of Photon based on frequency.

Part 2 - True or False

In a Single electron atom, energy of orbitals: 3s = 3p = 3d.

In a Multi electron atom, energy of orbitals: 3s = 3p = 3d.

In a Single electron atom, the effective nuclear charge experienced by an electron is always equal to the number of proton.

In a Multi electron atom, the effective nuclear charge experienced by an electron is always equal to the number of proton.

Z_eff is the effective nuclear charge experienced by an electron.

Based on the equation of Multi electron atom, the higher the Z_eff, the lower the energy (more negative).

In a Single electron atom:  Z effective of 3s = 3p = 3d.

In a Multi electron atom: Z effective of 3s > 3p > 3d.

λ_DB = h/mv This equation express the wave-length of a particle.

λ = c/v This equation express the wave-length of light.

Part 3 - Guided question

1) There is a convenient conversion that you can use in this class:

Energy(in eV) = (1240 nm.eV/λ(in nm))

This equation is equivalent to E = hc/λ

i) Calculate the λ of a photon with an energy of 5eV.

ii) Calculate the Energy of a photon with λ = 300 nm. Express answer in eV.

iii) Convert 20 eV to Joule.

2) Consider the quantum system below:

i) Calculate the energy of photon (in eV) emitted by an electron transitioning from C to B. SHOW APPROACH.

ii) Calculate the wavelength from of photon emitted by an electron transitioning from C to B.

iii) Calculate the wavelength of a photon emitted by an electron transitioning from C to A.

3) An electron in a Particle in a Box model initially at n = 4 absorb a photon to n = 7. The length of the box "L" is 4x10^-9m.

i) Calculate the energy of n=7. Express answer in Joule

ii) Calculate the energy of n=4. Express answer in Joule.

iii) Calculate the energy difference n=7 and n=4.

iv) Convert energy from Joule to eV.

v) Calculate the wavelength of photon necessary to excite the electron of PIB from n=4 to n=7.

4) For an Iron molecule (Fe), the effective nuclear charge are as follow:

Z_eff of 4s = 3.75 and Z_eff of 3d = 6.75

i) Calculate the energy of 4s electron (in eV).

ii) Calculate the energy of 3d electron (in eV).

iii) Calculate the energy of electron in Iron if n=∞.

iv) Calculate the energy difference of 4s and 3d orbital.

v) Calculate the wavelength of photon necessary to excite an electron in 4s orbital to 3d orbital.

vi) Ionization energy is a transition from an initial quantum state to n=∞. Calculate ionization energy of 4s and 3d electron in iron.

5) Drawing