Concept explainers
(a)
The transition in the Balmer series which produces the smallest frequency photon.
(a)
Answer to Problem 2SP
The transition in the Balmer series which produces the smallest frequency photon is
Explanation of Solution
Hydrogen spectrum lies in the visible, ultraviolet as well as infrared regions. Hydrogen spectrum is divided into different spectral series named as Lyman series, Balmer series, Paschen series, Brackett series and Pfund series. The wavelengths of lines in each series is determined using Balmer’s formula.
The Balmer’s formula is given as
From the Balmer’s formula it is clear that the photon having smallest frequency or longest wavelength will be emitted when the value of
Conclusion:
Thus the
(b)
The energy difference in joules for the two levels involved in the transition of part (a).
(b)
Answer to Problem 2SP
The energy difference in joules for the two levels involved in the transition of part (a) is
Explanation of Solution
Write the Balmer’s formula.
The value of
Substitute
Write the equation for the energy of a photon.
Here,
The value of
Substitute
The energy of the emitted photon is equal to the energy difference between the levels involved in the transition.
Conclusion:
Thus the energy difference in joules for the two levels involved in the transition of part (a) is
(c)
The frequency and wavelength of the photon emitted in the transition.
(c)
Answer to Problem 2SP
The frequency of the photon emitted in the transition is
Explanation of Solution
From part (b),
This gives,
Write the equation for the frequency of the photon.
Here,
Substitute
Conclusion:
Thus the frequency of the photon emitted in the transition is
(d)
The frequency and wavelength of the photon with the longest wavelength in the Lyman series.
(d)
Answer to Problem 2SP
The frequency of the photon with the longest wavelength in the Lyman series is
Explanation of Solution
The value of
Substitute
This gives,
Substitute
Conclusion:
Thus the frequency of the photon with the longest wavelength in the Lyman series is
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Chapter 18 Solutions
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