Question

An electron in a hydrogen atom jumps from the n = 3 state to the ground state. Which of the following statements can you deduce from this statement? (For convenience, note that a photon of wavelength 1240 nm has an energy of 1 eV.)A. The hydrogen atom has absorbed a photon of wavelength 82 nm.
B. The hydrogen atom emits a photon of wavelength 102.5 nm.
C. The hydrogen atom emits a photon of wavelength 210 nm.
D. The hydrogen atom has absorbed a photon of wavelength 102.5 nm.
E. The hydrogen atom emits a photon of wavelength 82 nm

Answer 1

Answer:

B) True. It is the photon is emitted the wavelength is correct

Explanation:

For this exercise let's use the Bohr model for the hydrogen atom

      Eₙ = -13.606 / n2

This gives the energy of the levels in eV. let's look for the energy  

n = 1

      E₁ = -13,606

n = 3

      E₃ = -13.606 / 3²

      E₃ = -1.512 eV

The transition occurs when moving from one level to another

     ΔE = E₃ -E₁

     ΔE = -1.512 + 13.606

    ΔE = 12.094 eV

Now let's use the Planck equation and the speed of light for the energy of the transition

    E = h F

    c = λ f

   E = h c / λ

   E = 6.63 10⁻³⁴ 3 10⁸ / λ

   E = 19.89 10⁻²⁶ /λ

  λ = 19.89 10⁻²⁶ / E

Let's reduce energy to July

   E = 12,094 eV (1.6 10⁻¹⁹ J / 1 eV) = 19.35 10⁻¹⁹ J

   λ = 19.89 10⁻²⁶ / 19.35 10⁻¹⁹

   λ = 1.0279 10⁻⁷ m

Let's reduce to nm

   λ = 1.0279 10⁻⁷ m (10⁹ nm / 1 m)

   λ = 102.79 nm

Let's examine the answers

A) False is another wavelength and the photon emitted

B) True. It is the photon is emitted the wavelength is correct

C) False. Wavelength is different

D) False the photon is emitted

E) False wavelength is different