If it takes 10.2 eV of energy excite hydrogen from the ground state into the first excited (n = 2) state, then what frequency photon is required to excite hydrogen out of the ground state into n = 2 state? What is the wavelength (lambda) of that photon? What kind of radiation (region of the electromagnetic spectrum) is this photon?

Question

If it takes 10.2 eV of energy excite hydrogen from the ground state into the first excited (n = 2) state, then what frequency photon is required to excite hydrogen out of the ground state into n = 2 state? What is the wavelength (

λ

) of that photon? What kind of radiation (region of the electromagnetic spectrum) is this photon?

Answer 1

The energy difference between the ground state and the first excited state is

Δ E = h v [1]

Use equation (1) to solve for the frequency of the photon.

v = \frac{Δ E}{h} = \frac{10.2 e V \times \frac{1.6 \times 10^{- 19} J}{1 e V}}{6.626 \times 10^{- 34} J \cdot s} = 2.463 \times 10^{15} [2]

The wavelength of the photon is

λ = \frac{c}{v} = \frac{3 \times 10^{8} m / s}{2.463 \times H z} = 1.218 \times 10^{- 7} m [3]

Answers (1)

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