Question

select the correct explanation wavelength as frequency increases from left to right across the electromagnetic spectrum above.
a energy does not affect the wavelength of radiation on the electromagnetic spectrum.
b wavelength decreases as energy remains the same across the electromagnetic spectrum.
c wavelength increases as energy increases across the electromagnetic spectrum.
d wavelength decreases as energy increases across the electromagnetic spectrum.

Explanation:

To solve this, we use the relationships in the electromagnetic spectrum: the formula for the energy of a photon is \( E = hf=\frac{hc}{\lambda} \) (where \( E \) is energy, \( h \) is Planck's constant, \( f \) is frequency, \( c \) is the speed of light, and \( \lambda \) is wavelength). From \( E=\frac{hc}{\lambda} \), we can see that energy (\( E \)) and wavelength (\( \lambda \)) are inversely proportional (when \( h \) and \( c \) are constant). Also, frequency (\( f \)) and wavelength (\( \lambda \)) are inversely proportional (\( c = f\lambda \)). So as frequency increases, energy increases (since \( E = hf \)) and wavelength decreases (from \( c = f\lambda \) or \( E=\frac{hc}{\lambda} \)).

• Option A is wrong because energy and wavelength are related.
• Option B is wrong because energy does not remain the same (energy increases with frequency, and frequency and wavelength are related, so energy changes with wavelength).
• Option C is wrong because wavelength and energy are inversely proportional, so wavelength should decrease as energy increases.
• Option D is correct as it states wavelength decreases as energy increases (consistent with \( E=\frac{hc}{\lambda} \)).

Answer:

D. Wavelength decreases as energy increases across the electromagnetic spectrum.