A student attempts to identify an unknown atomic gas by examining its bright-line…

PHYSICS · Multi-part · A Level · Physics · Particles and radiation · Particles and radiation

Problem

A student attempts to identify an unknown atomic gas by examining its bright-line emission spectrum. She measures three prominent lines at wavelengths 410 nm, 434 nm, and 656 nm. She hypothesizes that the gas might be hydrogen. The relevant bound-state energies (in electron-volts) for hydrogen and for a second candidate, element Y, are provided below. Hydrogen (selected levels): •

n=2: -3.40\,\text{eV}

•

n=3: -1.51\,\text{eV}

•

n=4: -0.85\,\text{eV}

•

n=5: -0.54\,\text{eV}

Element Y (selected levels): • Ground state:

-6.8\,\text{eV}

• Level a:

-4.2\,\text{eV}

• Level b:

-1.5\,\text{eV}

• Level c:

-0.62\,\text{eV}

(a) Calculate the photon energy for each of the three measured wavelengths. (b) Using the hydrogen energy levels, determine whether each of the calculated photon energies corresponds to an allowed transition that terminates at

n=2

. Show quantitative evidence. (c) Based on your analysis, state and justify whether the unknown gas is more likely to be hydrogen or element Y. (d) The student notices that no emission line is observed at 486 nm. Explain what the absence of this line suggests about the population of excited states in the gas under the conditions of the experiment.

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