Problem 115 - Chemistry: An Atoms-Focused Approach

Question

How does the wavelength of light required to ionize a gasphase atom change with increasing atomic number down a group in the periodic table?

Step-by-Step Solution

Answer

Answer: As the atomic number increases down a group in the periodic table, the wavelength of light required to ionize a gas-phase atom generally increases. This is due to the decrease in ionization energy as the atomic number increases.

Step 1: Understand Ionization Energy and Atomic Number

Ionization energy is the amount of energy required to remove an electron from an atom or ion, forming a cation. In general, ionization energy increases across a period from left to right and decreases down a group in the periodic table. As we go down a group, the atomic number increases, leading to a higher number of energy levels (shells) for electrons and an increased shielding effect, which results in a decrease in ionization energy.

Step 2: Understand the Relationship between Ionization Energy and Wavelength of Light

The energy of a photon of light is described by the Planck's equation: \(E = h \cdot f\) , where \(E\) is the energy of the photon, \(h\) is the Planck's constant (\(6.626 \times 10^{-34} Js\)), and \(f\) is the frequency of the light. Since the frequency is related to the wavelength by the speed of light \(c\) (where \(c = \lambda \cdot f\)), we can write the Planck's equation in terms of wavelength: \(E = \dfrac{h \cdot c}{\lambda}\), where \(\lambda\) is the wavelength of the light. If the energy of a photon of light is equal to the ionization energy of an atom, it can ionize the atom. Therefore, to find the wavelength of light required to ionize an atom, we can use the relationship: \(\lambda = \dfrac{h \cdot c}{E_{ionization}}\)

Step 3: Analyze the Change in Wavelength with Increasing Atomic Number

As the atomic number increases down a group in the periodic table, the ionization energy decreases due to the increased shielding effect and the increased number of electron energy levels (shells). According to the relationship \(\lambda = \dfrac{h \cdot c}{E_{ionization}}\), if the ionization energy decreases, the wavelength of light required to ionize the atom should increase. So, as the atomic number increases down a group in the periodic table, the wavelength of light required to ionize a gas-phase atom should generally increase.

Key Concepts

Photon Energy

Photon energy is crucial when discussing ionization. When we talk about photons, we're referring to tiny packets of light energy. They have specific energy levels determined by their frequency. The higher the frequency, the higher the energy. This relationship is captured by Planck’s equation: \[E = h \cdot f\] Here, \(E\) stands for photon energy, \(h\) is Planck's constant \((6.626 \times 10^{-34} \, \text{Js})\), and \(f\) represents frequency.
In ionization, a photon must have enough energy to remove an electron from an atom. If the photon's energy matches the ionization energy of the atom, it can effectively "kick out" an electron, causing ionization. As we delve further into the concepts, we'll see how energy, frequency, and wavelength are interconnected.
Understanding how photon energy works is fundamental in realizing why different elements require different energies to be ionized.

Wavelength and Frequency

The relationship between wavelength and frequency is key to understanding light's behavior. Wavelength \((\lambda)\) and frequency \((f)\) are inversely related to each other through the speed of light \((c)\) with the equation:\[c = \lambda \cdot f\]This means when one value increases, the other decreases. In simpler terms, if a wave has a short wavelength, it has a high frequency and vice versa.
Photon energy comes into play again here. Using the equation:\[E = \frac{h \cdot c}{\lambda}\]we can understand that energy is also inversely related to wavelength. High-energy photons have short wavelengths and high frequency.
In the context of ionization, as you go down a group in the periodic table, ionization energy decreases. As a result, the wavelength required to ionize an atom becomes longer. More on why this happens in the periodic table trends section.

Periodic Table Trends

Understanding periodic table trends helps in grasping how ionization energy varies across different elements. The periodic table is organized in a way that allows us to predict these trends effectively. As you move down a group in the periodic table, two main factors alter ionization energy:

• Increased Energy Levels: More electron shells are added, making outer electrons farther from the nucleus.
• Greater Shielding Effect: Inner shells of electrons shield the outer electrons from the nucleus, reducing attraction.

Both factors lead to decreased ionization energy. Therefore, less energy is needed to remove an electron from an atom.
Returning to our context of ionization, as the ionization energy decreases down a group due to these trends, the wavelength of light needed to ionize the atom increases.
These insights are essential for predicting the behavior of atoms in different groups when exposed to light, illustrating how periodical trends can be powerful predictive tools.