Question 18.3: Sample Exercise: Energy Levels in a Hydrogen Atom Using the ...
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 = ?
The energy difference is
ΔE = E_{4} – E_{2}
= -0.85 eV – (-3.4 eV)
= 2.55 eV
Using h = 6.626 × 10^{-34} J·s = 4.14 × 10^{-15} eV·s,
the frequency of the emitted photon is given by
E = hf
f=\frac{2.55 eV}{4.14 × 10^{-15} eV.s}
= 6.16 × 10^{14} Hz
From v = c = fλ, the wavelength of the emitted photon is then
λ=\frac{c}{f}=\frac{3 × 10^{8} m/s}{6.16 × 10^{14} Hz}
=4.87 × 10^{-7} m= 487 nm
This is the blue line in the Balmer series of the hydrogen spectrum, pictured in figure 18.17.
Related Answered Questions
Question: 18.4
Verified Answer:
p = mv λ=\frac{h}{p}[/l...
Question: 18.2
Verified Answer:
\frac{1}{λ}= R (\frac{1}{n^{2}}-\frac{1}{m^...
Question: 18.1
Verified Answer:
The reaction can be described by the reaction equa...