How to Calculate the Wavelength of a Photon during a Transition in a Hydrogen-like Atom/Ion – Part 1

The Planck relation (aka Planck's energy–frequency relation, the Planck–Einstein relation, or Planck equation) is a fundamental equation in quantum mechanics which states that the energy difference ΔE in an atomic electron transition is proportional to the photon frequency ν, i.e., ΔE = hν (h = Planck constant).


The photon velocity c is related to ν & photon wavelength λ as c = νλ.

ΔE of an electron during a transition from the initial state ni to the final state nf in an H-like atom is expressed as:

ΔE = 2.18 x 10─18 Z2 (1/ni2 ─ 1/nf2) J/electron (Z = Atomic number)

Question:

What is the wavelength of a photon emitted during a transition from n = 5 state to the n = 2 state in the H atom?

Solution:



Click/tap to enlarge the image

This transition gives rise to a spectral line in the visible region of the Balmer series.

Exciting electron transition❓ Let Chemaficionado know in the comments below or at mychemistryhomework@gmail.com❗

References:

(1)    Brown, C.; Ford, M. Higher Level Chemistry, 2nd ed.; Pearson Education: Harlow, Essex, 2014.

(2)    Wikipedia. Planck Relation. Wikipedia. https://en.wikipedia.org/wiki/Planck_relation.

(3)    Ncert. Chemistry : Textbook for Class XI - Part.I; National Council Of Educational Research And Training: New Delhi.

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