Sample Exercise: Energy Levels in a Hydrogen Atom
Using the energy values shown in figure 18.20, calculate the wavelength of the photon emitted in the transition from the n = 4 energy level to the n = 2 energy level in the Bohr model of the hydrogen atom.

$E_{2} = -3.4$ eV
$E_{4} = -0.85$ eV
λ = ?

Question

Sample Exercise: Energy Levels in a Hydrogen Atom
Using the energy values shown in figure 18.20, calculate the wavelength of the photon emitted in the transition from the n = 4 energy level to the n = 2 energy level in the Bohr model of the hydrogen atom.

[latex]E_{2} = -3.4[/latex] eV
[latex]E_{4} = -0.85[/latex] eV
λ = ?

Accepted Answer

The energy difference is

[latex]ΔE = E_{4} - E_{2}[/latex]
= -0.85 eV - (-3.4 eV)
= 2.55 eV
Using [latex]h = 6.626 × 10^{-34}[/latex] J·s [latex]= 4.14 × 10^{-15}[/latex] eV·s,
the frequency of the emitted photon is given by
E = hf

[latex]f=\frac{E}{h} [/latex]

[latex]f=\frac{2.55 eV}{4.14 × 10^{-15} eV.s} [/latex]

[latex]= 6.16 × 10^{14}[/latex] Hz

From v = c = fλ, the wavelength of the emitted photon is then

[latex]λ=\frac{c}{f} [/latex]

[latex]=\frac{3 × 10^{8} m/s}{6.16 × 10^{14} Hz}[/latex]

[latex]=4.87 × 10^{-7} m= 487 nm[/latex]

This is the blue line in the Balmer series of the hydrogen spectrum, pictured in figure 18.17.

Question 18.3: Sample Exercise: Energy Levels in a Hydrogen Atom Using the ...

Related Answered Questions

Sample Exercise: Finding the Wavelength of a Baseball What is the de Broglie wavelength, in meters, of a 145 g baseball traveling at 80 mph? ...

Verified Answer:

Sample Exercise: Using the Rydberg Formula What is the wavelength of the photon in the infrared series of the hydrogen spectrum for m = 6 and n = 3? Use the Rydberg formula. R = 1.097 × 10^7 m^-1 ...

Verified Answer:

Sample Exercise: Burning Carbon If 30 g of pure carbon are burned (combined with oxygen) to form carbon dioxide, how many grams of oxygen will be consumed in this reaction? Carbon has an atomic mass of 12, and oxygen has an atomic mass of 16. ...

Verified Answer: