Light as Electromagnetic Radiation (4D) - MCAT Chemical and Physical Foundations of Biological Systems

Speed decreases; frequency stays constant; wavelength decreases. Upon entering a denser medium, light speed decreases while frequency remains constant, resulting in shorter wavelength.

$c = \lambda f$. The wave speed in vacuum equals the product of wavelength and frequency for electromagnetic radiation.

A transverse wave; $\vec{E}$ and $\vec{B}$ are perpendicular to propagation. Electromagnetic waves are transverse because the electric and magnetic fields oscillate perpendicular to the direction of wave propagation.

$v = 2.0\times 10^8\ \text{m/s}$. Speed in the medium is vacuum speed divided by the refractive index of glass, yielding the given velocity.

$\lambda = 310\ \text{nm}$. Wavelength in nm is found by dividing $hc$ by energy in eV, producing the indicated wavelength.

$E = 2.0\ \text{eV}$. Photon energy in eV is obtained by dividing $hc$ by wavelength in nm, giving the stated energy.

$f = 5.0\times 10^{14}\ \text{Hz}$. Frequency is determined by dividing speed of light by wavelength, resulting in the specified value.

$K_{\max} = hf - \phi$. In the photoelectric effect, maximum kinetic energy is incident photon energy minus the work function.

$\phi = hf_0$. The work function equals the energy of photons at the threshold frequency for electron emission.

$p = \frac{E}{c}$. For photons, relativistic energy-momentum relation simplifies to momentum as energy divided by speed of light.

$p = \frac{h}{\lambda}$. Photon momentum arises from wave-particle duality, equaling Planck's constant divided by wavelength.

$I \propto \frac{1}{r^2}$. Intensity follows the inverse square law as power spreads over the surface area of an expanding sphere.

$f \propto \frac{1}{\lambda}$ because $v = \lambda f$ with fixed $v$. With constant wave speed in a medium, frequency and wavelength maintain an inverse proportionality.

$\sin\theta_c = \frac{n_2}{n_1}$. The critical angle occurs when the refracted angle is 90 degrees, leading to total internal reflection for larger incident angles.

Light must go from higher to lower $n$: $n_1 > n_2$. Total internal reflection requires light traveling from a medium of higher refractive index to one of lower index.

$c \approx 3.0 \times 10^8\ \text{m/s}$. This value represents the constant speed at which light travels in vacuum, fundamental for wave calculations.

$n_1\sin\theta_1 = n_2\sin\theta_2$. Snell's law governs refraction by equating the products of refractive indices and sines of angles across an interface.

$n = \frac{c}{v}$. Refractive index quantifies the reduction in light speed within a medium relative to vacuum.

Photon energy increases because $E \propto \frac{1}{\lambda}$. Photon energy is inversely proportional to wavelength, so decreasing wavelength increases energy.

Radio < microwave < IR < visible < UV < X-ray < gamma. The electromagnetic spectrum is ordered by increasing frequency, which corresponds to increasing energy and decreasing wavelength.

$hc \approx 1240\ \text{eV}\cdot\text{nm}$. This product enables straightforward computation of photon energy in electronvolts from wavelength in nanometers.

$h \approx 6.6 \times 10^{-34}\ \text{J}\cdot\text{s}$. This approximate value of Planck's constant is used in quantum mechanics calculations for energy-frequency relations.

$E = \frac{hc}{\lambda}$. Derived from $E=hf$ and $c=lambda f$, photon energy is inversely proportional to wavelength.

$E = hf$. Photon energy is directly proportional to its frequency, with Planck's constant as the proportionality factor.