Chapter.17 Atom//Course

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An atom, given in its fundamental state, absorbs a photon . Correct the false sentence.

1.1 - The atom stays in its fundamental state.

1.2 - The fundamental state is associated to the level n = 2.

1.3 - The atom undergoes a deexcitation.

1.4 - The minimum value of the absorbed energy that can excite this atom is E₂ - E₁.

1.5 - A photon of energy E_ph < E₂ - E₁ is absorbed by this atom.

1.6 - A photon of energy E > E₂ - E₁ is necessarily absorbed by this atom.

1.7 - The true answer of part 1.6 verifies the quantization of energy of the atom.

1.8 - The energy of the atom in the ionized state is E = 0.

1.9 - The ionization energy of an atom is E₁.

1.10 - The transition from n = 1 to n = 3 needs the absorption of a photon of energy E₃.

Given: Planck's constant 6.63 × 10^-34 J·s; speed of light in vacuum

 3 × 10⁸ m/s.

            

          

Answers

Knowing that the specific energies of the H atom are given by E_n = 13.6/n² in eV; and the H atom is given in its fundamental state.  Correct the false sentence.

1. The energy of the H atom in the 2^nd excited state is -3.4 eV.
2. This atom needs at least an energy of 10.2 eV to be excited.
3. If the atom undergoes the transition from n = 4 to n = 1, we say that it is excited to the excited level n = 1.
   
   
   
4. Absorbing an energy equal to E₄ - E₁, this atom will be excited to the third excited level.
5. If the atom undergoes the transition from n = 4 to n = 1, we say that it will be excited to the level n = 1.
6. The H atom, passing from level n = 4 to n = 1, absorbs a photon.
7. The H atom undergoes the transition from n = 3 to n = 2. The emitted radiation has a wavelength λ₃₂ = 120 nm.
8. The H atom, when deexcited from level n = 3 to n = 2, emits a visible radiation.
9. The H atom, given in its fundamental state, receives four photons of respective energies: 10 eV, 10.4 eV, 12.09 eV and 13.8 eV. Specify the energetic state of the atom after receiving each photon.
10. An H atom, in its fundamental state, receives a particle (an electron for example) of kinetic energy 10.4 eV.
    10.1 What will be the new state of the atom?
    10.2 By comparing the result with question 9, explain the difference between particle and photon.

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     Answer to question 2.9   Part B

The Rydberg formula applies only to hydrogen atoms. It allows us to calculate the wavelengths of radiation that can be emitted or absorbed by the H atom.

Given: Planck's constant h = 6.63×10^-34 J·s; speed of light in vacuum c = 3×10⁸ m/s

1.1) Write the Rydberg formula corresponding to the transition from m to p with p > m.

1.2) Calculate the wavelength for the hydrogen transition from n = 5 to n = 2.

1.3) Is the radiation emitted in question 1.2 visible? To which series does it belong?

1.4) Use the Rydberg formula to verify that the energy of the hydrogen atom in energy state n is given by: E_n = -13.6/n² eV.

1.5) What transitions compose the Balmer series? What special property do the radiations associated with these transitions have for the H atom?

1.6) Transitions from n > 1 to n = 1 correspond to which series? To which domain do they belong for the H atom (Visible, UV, or IR)?

1.7) What transitions compose the Paschen series? To which domain do they belong for the H atom (Visible, UV, or IR)?

1.8) An atom is characterized by the energy diagram given in document (2). It is in the energy state E₂. Can this atom absorb a photon of energy 1.99 eV?

1.9) For the atom in question 1.8, when deexciting from n = 3 to the lowest levels, show with arrows the possible transitions.

1.10) Conversely, if the previous atom undergoes excitation from the ground state to the 3rd excited state, show this transition with an arrow.

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