Final answer:
When plotting a graph of energy difference against the reciprocal of the wavelength, which reflects the frequency, the result is a straight line due to the direct proportionality between energy and frequency, and inverse proportionality between energy and wavelength.
Step-by-step explanation:
If you plot a graph of energy difference versus the reciprocal of the wavelength (which is proportional to frequency), according to the relationship between energy, frequency, and wavelength in physics, you will get a straight line. This is because the energy (E) of electromagnetic radiation is directly proportional to its frequency (f) and inversely proportional to its wavelength (λ). Planck's formula, which is E = hν (where h is Planck's constant and ν is the frequency), further illustrates this direct proportionality as frequency increases with a decrease in wavelength, implying that if you have the reciprocal of the wavelength on one axis and energy difference on the other, it will form a straight-line graph.
This straight-line relationship is a result of how these quantities are related in physics. The energy carried by a wave is proportional to its frequency and, therefore, inversely proportional to its wavelength. In spectroscopy, frequency is often expressed in different units, such as cm²¹, but the inverse proportionality remains. In practice, as frequency increases (meaning the wavelength decreases), the energy associated with the radiation also increases, which is depicted as a straight line on a graph where both axes are logarithmic, known as a log-log plot.