A monochromatic beam of light is absorbed by a collection of ground-state hydrog

Question

A monochromatic beam of light is absorbed by a collection of ground-state hydrogen atoms in such a way that three different wavelengths are observed when the hydrogen relaxes back to the ground state.

(a) What is the wavelength of the incident beam?

This is the wavelength of the photon that will ionize the atom. There are then an infinite number of ways for the electron to return to the ground state. nm

Explain the steps in your solution.

(b) What is the longest wavelength in the emission spectrum of these atoms?
nm

(c) To what portion of the electromagnetic spectrum does it belong?
infared, visible, ultraviolet?

(d) To what series does it belong?
Lymen, Balmer, Paschen?

(e) What is the shortest wavelength?
nm

(f) To what portion of the electromagnetic spectrum does it belong?
infared, visible, ultraviolet

(g) To what series does it belong?

lymen, balmer, paschen

Explanation / Answer

The 3 would have to be - level 2 to level 1 ( ground state ) ( and a UV frequency )
Level 3 to level 1 (another, slightly higher UV )
Level 3 to level 1 ( the hydrogen alpha line - red )

So the incident photons have the energy to "raise" the electron from ground state to level 3.

Ei = -13.6/ 1^2 = -13.6 eV

Ef = -13.6/ 3^2 = -1.51

so the incoming photons have wavelength = c/f = hc/ E(photon)

Wavelength = (hc)/ (Ef-Ei) = (6.626*10^-34 * 3*10^8) / ( -1.51 + 13.6 ) = 1.64 * 10^-26

(1.64 * 10^-26) / (1.6 * 10^-19) = 102.5 nm

The longest of the six wavelengths corresponds to the lowest photon energy, emitted in the 3 to 2 transition

Ei = -13.6/ 3^2 = -1.51 eV

Ef = -13.6/ 2^2 = -3.4 eV

Wavelength = 1240 eV.nm / (3.4 - 1.51) = 656.084656 nm

The shortest wavelength emitted is the same as the wavelength absorbed: 102.5 nm

UV spectrum, lymen series for both

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects