The Balmer series of the hydrogen spectrum corresponds to electronic transitions that…
CHEMISTRY · Multi-part · CBSE · Chemistry · Structure of Atom · Structure of Atom
Problem
The Balmer series of the hydrogen spectrum corresponds to electronic transitions that end in the state n=2. The table below lists the measured wavelengths for three such transitions.
Initial quantum number ni | Measured wavelength λ (nm)
3 | 656
4 | 486
5 | 434
A student wishes to use these data to estimate a constant that characterises the spectral lines of hydrogen.
(a) Compute the reciprocal wavelength 1/λ for each transition and record the results in a clear, labeled table.
(b) The student plots 1/λ (vertical axis) versus 1/ni2 (horizontal axis). Describe the expected shape of the graph and explain the reasoning behind your expectation.
(c) Using the three data points, determine the slope of the best-fit straight line and hence obtain a numerical estimate for the constant that appears in the linear relationship.
(d) Employ your estimated constant to predict the wavelength of the photon produced in the transition ni=6→nf=2. Compare your prediction with the commonly accepted experimental value of 410nm and comment on possible sources of discrepancy.