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Difficulty: EasyEnergy Levels and Atomic Spectra

An electron in an excited atom transitions from an energy level of −2.5 eV-2.5\text{ eV} to a lower energy level of −8.5 eV-8.5\text{ eV}. What is the energy of the emitted photon in Joules? (1 eV=1.6×10−19 J1\text{ eV} = 1.6 \times 10^{-19}\text{ J})

  1. 9.6×10−19 J9.6 \times 10^{-19}\text{ J}Answer
  2. B
    6.0×10−19 J6.0 \times 10^{-19}\text{ J}
  3. C
    1.76×10−18 J1.76 \times 10^{-18}\text{ J}
  4. D
    −9.6×10−19 J-9.6 \times 10^{-19}\text{ J}

Answer

The energy of the emitted photon is 9.6×10−19 J9.6 \times 10^{-19}\text{ J}.
The energy of the emitted photon is given by ΔE=Ei−Ef=−2.5 eV−(−8.5 eV)=6.0 eV\Delta E = E_i - E_f = -2.5\text{ eV} - (-8.5\text{ eV}) = 6.0\text{ eV}. Converting this to Joules gives 6.0×1.6×10−19 J=9.6×10−19 J6.0 \times 1.6 \times 10^{-19}\text{ J} = 9.6 \times 10^{-19}\text{ J}.

Step-by-Step Solution

1
Calculate the energy difference ΔE\Delta E between the initial and final energy levels.
ΔE=Einitial−Efinal=−2.5 eV−(−8.5 eV)=6.0 eV\Delta E = E_{\text{initial}} - E_{\text{final}} = -2.5\text{ eV} - (-8.5\text{ eV}) = 6.0\text{ eV}.
When an electron drops to a lower energy state, it emits a photon with energy equal to the difference between the two energy levels.
2
Convert the energy from electron-volts (eV) to Joules (J).
E=6.0 eV×1.6×10−19 J/eV=9.6×10−19 JE = 6.0\text{ eV} \times 1.6 \times 10^{-19}\text{ J/eV} = 9.6 \times 10^{-19}\text{ J}.
Standard SI unit calculations require multiplying the value in eV by 1.6×10−19 J/eV1.6 \times 10^{-19}\text{ J/eV}.

Key Concept

Photon Emission during Atomic Transitions
Estimated Time:45s
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Topics

Energy Levels and Atomic Spectra

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