Multiple Choice
Using the Balmer formula for hydrogen, what is the wavelength (in nm) of the spectral line produced when an electron transitions from n = 8 to n = 2?
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9. Quantum Mechanics
Wavelength and Frequency
Multiple Choice
Which graph most accurately displays the relationship between the energy and frequency of a photon?
A
A horizontal line indicating constant energy regardless of frequency
B
A straight line with a negative slope
C
A straight line with a positive slope passing through the origin
D
A curve that increases rapidly at low frequencies and levels off at high frequencies
Verified step by step guidance1
Recall the fundamental relationship between the energy of a photon and its frequency, which is given by the equation \(E = h \nu\), where \(E\) is the energy, \(h\) is Planck's constant, and \(\nu\) (nu) is the frequency.
Understand that Planck's constant \(h\) is a positive constant, so the energy \(E\) is directly proportional to the frequency \(\nu\).
Recognize that a direct proportionality between two variables means the graph of energy versus frequency will be a straight line passing through the origin (0,0) with a positive slope equal to \(h\).
Eliminate options that do not fit this relationship: a horizontal line (constant energy) contradicts direct proportionality, a negative slope implies energy decreases with frequency, and a curve that levels off does not represent a linear relationship.
Conclude that the graph showing a straight line with a positive slope passing through the origin most accurately represents the relationship between photon energy and frequency.
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