Question
According to the equation for the Balmer line spectrum of hydrogen, a value of $n=4$ gives a red spectral line at $486.1 \mathrm{~nm} .$ Calculate the energy in kilojoules per mole of the radiation corresponding to this spectral line.
Step 1
Step 1: We start by using the equation for the energy of a photon, which is given by $E = h \cdot c / \lambda$, where $h$ is Planck's constant, $c$ is the speed of light, and $\lambda$ is the wavelength of the light. Show more…
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According to the equation for the Balmer line spectrum of hydrogen, a value of $n=3$ gives a red spectral line at $656.3 \mathrm{nm},$ a value of $n=4$ gives a green line at $486.1 \mathrm{nm},$ and a value of $n=5$ gives a blue line at 434.0 nm. Calculate the energy in kilojoules per mole of the radiation corresponding to each of these spectral lines.
Use the Balmer equation to calculate the wavelength in nanometers of the spectral line for hydrogen when $n=6$ What is the energy in kilojoules per mole of the radiation corresponding to this line?
One series of lines of the hydrogen spectrum is caused by emission of energy accompanying the fall of an electron from outer shells to the fourth shell. The lines can be calculated using the Balmer-Rydberg equation: $$ \frac{1}{\lambda}=R_{\infty}\left[\frac{1}{m^{2}}-\frac{1}{n^{2}}\right] $$ where $m=4, R_{\infty}=1.097 \times 10^{-2} \mathrm{~nm}^{-1}$, and $n$ is an integer greater than $4 .$ Calculate the wavelengths in nanometers and energies in kilojoules per mole of the first two lines in the series. In what region of the electromagnetic spectrum do they fall?
Periodicity and the Electronic Structure of Atoms
Electron Configurations and Periodic Properties: Atomic Radii
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