MCAT Physics and Math Review

Chapter 9: Atomic and Nuclear Phenomena

Introduction

All of life depends on the photoelectric effect. As a photon of light enters the chloroplast in a plant cell, it reacts with chlorophyll, causing the ejection of an electron from certain magnesium-containing dyes. This electron feeds into synthetic pathways that ultimately result in glucose production. While the MCAT does not include photosynthesis in its content lists, its principles are a primary example of the photoelectric effect. It was Albert Einstein who described this effect, and it was this that won him the Nobel Prize—not the theory of relativity. We now use the photoelectric effect in many industrial applications, such as solar panels.

After discussing the photoelectric effect, we will examine nuclear radiation. Nuclear radiation is curiously full of opposites: it can cause life-threatening diseases such as cancer, but it can also be used in the treatment of cancer. It can be used safely for mass power generation, but it can cause untold devastation in meltdowns or weapons of mass destruction. In addition to nuclear radiation, we will examine the strong nuclear force and the equation of mass defect, perhaps the most quoted equation in all of science. At the end of this chapter, we’ll have covered all of the physics content tested on the MCAT, and be ready to move on to mathematics and some skills-based practice.

9.1 The Photoelectric Effect

When light of a sufficiently high frequency (typically, blue to ultraviolet light) is incident on a metal in a vacuum, the metal atoms emit electrons. This phenomenon, discovered by Heinrich Hertz in 1887, is called the photoelectric effect. As mentioned above, Albert Einstein’s 1905 explanation of the photoelectric effect won him the Nobel Prize.

Electrons liberated from the metal by the photoelectric effect will produce a net charge flow per unit time, or current. Provided that the light beam’s frequency is above the threshold frequency of the metal, light beams of greater intensity produce larger current in this way. The higher the intensity of the light beam, the greater the number of photons per unit time that fall on an electrode, producing a greater number of electrons per unit time liberated from the metal. When the light’s frequency is above the threshold frequency, the magnitude of the resulting current is directly proportional to the intensity (and amplitude) of the light beam.

THRESHOLD FREQUENCY

The minimum frequency of light that causes ejection of electrons is known as the threshold frequencyfT. The threshold frequency depends on the type of metal being exposed to the radiation. The photoelectric effect is, for all intents and purposes, an “all-or-nothing” response: if the frequency of the incident photon is less than the threshold frequency (f < fT), then no electron will be ejected because the photons do not have sufficient energy to dislodge the electron from its atom. But if the frequency of the incident photon is greater than the threshold frequency (f > fT),then an electron will be ejected, and the maximum kinetic energy of the ejected electron will be equal to the difference between hf and hfT (also called the work function). Einstein’s explanation of these results was that the light beam consists of an integral number of light quanta calledphotons. The energy of each photon is proportional to the frequency of the light:

E = hf

Equation 9.1

Where E is the energy of the photon of light, h is Planck’s constant (6.626 × 10−34 J · s), and f is the frequency of the light. Once we know the frequency, we can easily find the wavelength λ according to the equation c = f λ, as described in Chapter 8 of MCAT Physics and Math Review. According to these equations, waves with higher frequency have shorter wavelengths and higher energy (toward the blue and ultraviolet end of the spectrum); waves with lower frequency have longer wavelengths and lower energy (toward the red and infrared end of the spectrum). In nuclear physics, wavelength is commonly measured in nanometers (1 nm = 10−9 m) and ångströms (1 Å = 10−10 m).

KEY CONCEPT

The energy of a photon increases with increasing frequency. The reason that we only discuss electrons being ejected from metals (and not protons or neutrons) is because of the weak hold that metals have on their valence electrons due to their low ionization energies.

KINETIC ENERGY OF EJECTED ELECTRONS

If the frequency of a photon of light incident on a metal is at the threshold frequency for the metal, the electron barely escapes from the metal. However, if the frequency of an incident photon is above the threshold frequency of the metal, the photon will have more than enough energy to eject a single electron, and the excess energy will be converted to kinetic energy in the ejected electron. We can calculate the maximum kinetic energy of the ejected electron with the formula:

Kmax = hf − W

Equation 9.2

where W is the work function of the metal in question. The work function is the minimum energy required to eject an electron and is related to the threshold frequency of that metal by:

WhfT

Equation 9.3

These formulas solve for the maximum kinetic energy of the electron rather than exact kinetic energy because the actual energy can be anywhere between 0 and Kmax, depending on the specific subatomic interactions between the photon and the metal atom. Kmax is only achieved when all possible energy from the photon is transferred to the ejected electron.

MCAT EXPERTISE

The photoelectric effect is not frequently tested on the MCAT, but the underlying principles are simple. This is simply another example of energy transfer in which light energy causes an increase in electrical potential energy in the atom—enough to allow the electron to escape. If any energy is “left over,” it cannot be destroyed. Rather, it is transferred into kinetic energy in the ejected electron.

BRIDGE

Think of the work function like activation energy, in the sense that it must be matched or exceeded to cause the reaction (escape of an electron) to occur. Activation energy is discussed in Chapter 5 of MCAT General Chemistry Review.

Example:

If blue light of frequency 6.00 × 1014 Hz is incident on rubidium (W = 2.26 eV), will there be photoejection of electrons? If so, what is the maximum kinetic energy that an ejected electron will carry away? (Note:

h = 6.626 × 10−34 J · s = 4.14 × 10−15 eV · s)

Solution:

If the photons have a frequency of 6.00 × 1014 Hz, each photon has an energy of:

E = hf= (4.14 × 10−15 eV · s)(6.00 × 1014 Hz) = 2.48 eV

Clearly then, any given photon has more than enough energy to allow an electron in the metal to overcome the 2.26 eV barrier. In fact, the maximum excess kinetic energy carried away by the electron turns out to be:

K = hf − W= 2.48 − 2.26 = 0.22 eV

In general, the photoelectric effect is strong support for the particle theory of light, which states that light is not a continuous wave but acts as discrete bundles of energy called photons, as shown in Figure 9.1.

Figure 9.1. The Photoelectric Effect

MCAT Concept Check 9.1:

Before you move on, assess your understanding of the material with these questions.

1.    How does the work function relate to the energy necessary to emit an electron from a metal?

2.    What does the threshold frequency depend upon?

3.    What electrical phenomenon results from the application of the photoelectric effect?