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statuscvo [17]
3 years ago
7

Doubly ionized lithium Li2+ (Z = 3) and triply ionized beryllium Be3+ (Z = 4) each emit a line spectrum. For a certain series of

lines in the lithium spectrum, the shortest wavelength is 40.5 nm. For the same series of lines in the beryllium spectrum, what is the shortest wavelength?
Physics
1 answer:
EleoNora [17]3 years ago
6 0

Answer:

tex]\lambda_{Be}[/tex] = 22.78 nm

Explanation:

Bohr's model for the hydrogen atom has been used by other atoms with a single electric charge by changing the number of charges by the charge of the new atom (atomic number)

      E_{n}= k e² / 2a₀ (1 /n²)

      ao = h'² / k m e²               h' = h/2πi

For another atom with a single electron in the last layer

      a₀ ’= h’² / k m (Ze)²  

      a₀ ’= a₀ / Z²

Therefore, when replacing in the equation

      E_{n} = - Z²  Eo/n²

     E₀ = 13,606 eV

The transition occurs when the electron stops from one level to another

         E_{n} -  E_{m} = Z² E₀ (1 / n² - 1 / m²) = Z² ΔE

Let's relate this expression to the wavelength

       c = λ f

      E = h f

      E = h c /λ

      h c / λ = Z² ΔE

     λ = 1 / Z² (hc / ΔE)

     λ = 1 / Z² λ_hydrogen

Let's apply this last equation to our case

Lithium Z = 3

     E_{n} = - 9 Eo / n²

     

      40.5 10-9 = 1/9 λ_hydrogen

Beryllium Z = 4

      λ = 1/16 λ_hydrogen

Let's write our two equations is and solve

     40.5 10-9 = 1/9 λ_hydrogen

    tex]\lambda_{Be}[/tex] = 1/ 16 λ_hydrogen

      40.5 10⁻⁹ = 1/9 (16 \lambda_{Be} )

    tex]\lambda_{Be}[/tex] = 40.5 9/16

  tex]\lambda_{Be}[/tex] = 22.78 nm

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D
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<u>Hello and Good Morning/Afternoon</u>:

<em>Original Question: C₂H₅OH + __O₂ → __CO₂ + __ H₂O</em>

<u>To balance this equation</u>:

⇒ must ensure that there is an equal number of elements on both sides of the equation at all times

<u>Let's start balancing:</u>

  • On the left side of the equation, there are 2 carbon molecule

              ⇒ but only so far one on the right side

         C<em>₂H₅OH + __O₂ →  2CO₂ + __ H₂O</em>

  • On the left side of the equation, there are 6 hydrogen molecules

               ⇒ but only so far two on the right side

         C<em>₂H₅OH + __O₂ →  2CO₂ + 3H₂O</em>

  • On the right side of the equation, there are 7 oxygen molecules

                ⇒ but only so far three on the left side

         C<em>₂H₅OH + 3O₂ →  2CO₂ + 3H₂O</em>

<u>Let's check and make sure we got the answer:</u>

                           C<em>₂H₅OH + 3O₂ →  2CO₂ + 3H₂O</em>

<em>                 2 Carbon                ⇔                    2 Carbon</em>

<em>                 6 Hydrogen            ⇔                   6 Hydrogen</em>

<em>                 7 Oxygen                ⇔                   7 oxygen</em>

<u>Thefore the coefficients in order are</u>:

  ⇒ 1, 3, 2, 3

<u>Answer: 1,3,2,3</u>

Hope that helps!

#LearnwithBrainly<em>                      </em>

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Interference fringe refers to bands caused by different lights which can be found in phase or not each other.

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