Concept explainers
(a)
To show that the difference in wavelength between the hydrogen-1 and deuterium spectral lines associated with a particular electron transition is
(a)
Answer to Problem 13P
The difference in wavelength between the hydrogen-1 and deuterium spectral lines associated with a particular electron transition is
Explanation of Solution
Write the general expression for the energy levels of one electron atoms.
Here,
Refer the above equation and write an expression for energy released for any transition in hydrogen-1 or proton atom.
Here,
Refer the above equation and write an expression for energy released for any transition in hydrogen-2 or deuterium atom.
Here,
Write the formula for the reduced mass of proton atom.
Here,
Write the formula for the reduced mass of the deuterium atom.
Here,
Divide equation (I) and (II).
Energy is inversely proportional to the wavelength. Thus re-write the above equation.
Here,
Re-write the above equation.
Conclusion:
The difference in wavelength between the hydrogen-1 and deuterium spectral lines associated with a particular electron transition is
(b)
The wavelength difference for the Balmer alpha line of hydrogen emitted from a transition from
(b)
Answer to Problem 13P
The wavelength difference for the Balmer alpha line of hydrogen emitted from a transition from
Explanation of Solution
Refer section (a) and write the formula for the ration of the reduced mass of proton.
Here,
Write the formula for the reduced mass of the deuterium atom.
Here,
Write the formula for the ration of reduced mass of proton and deuterium.
Write the formula for the difference in wavelength of proton and deuterium.
Conclusion:
Substitute
Substitute
The wavelength difference for the Balmer alpha line of hydrogen emitted from a transition from
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Chapter 41 Solutions
Physics for Scientists and Engineers with Modern Physics
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