Two closely spaced ultraviolet lines are detected from a gas containing a single…

CHEMISTRY · Subjective · CBSE · Chemistry · Structure of Atom · Structure of Atom

Problem

Two closely spaced ultraviolet lines are detected from a gas containing a single species of hydrogen-like ions. The lines correspond to the Balmer

\beta

transition (

n=4 \rightarrow n=2

) and the Balmer

\gamma

transition (

n=5 \rightarrow n=2

). Measured wavelengths (with estimated uncertainty) are:

\lambda_{\beta} = 30.38 \pm 0.05\,\text{nm}

\lambda_{\gamma} = 27.13 \pm 0.05\,\text{nm}

. (The wavelengths of the same lines in hydrogen are

486.1\,\text{nm}

and

434.0\,\text{nm}

respectively.) (a) Determine the atomic number

Z

obtained from each line separately. (b) Taking the individual results and their uncertainties into account, calculate the weighted mean value of

Z

. (c) Propagate the given measurement uncertainties to estimate the percentage error in your final value of

Z

. (d) Using the periodic table, identify the ion that most plausibly matches your result and comment briefly on the agreement between experiment and theory.

Related theory

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