S1.3.6 Ionization energy (Higher Level Only)

The Limit of Convergence and Trends in Ionization Energy

1. Picture yourself at a fireworks display.
2. The dazzling colors you enjoy are caused by electrons in metal ions absorbing energy, jumping to higher energy levels, and then releasing that energy as light when they return to lower levels.
3. But have you ever wondered: what happens if an electron absorbs so much energy that it escapes the atom entirely?

This process, called ionization, is key to understanding the concept of convergence in emission spectra and the periodic trends in ionization energy.

The Limit of Convergence in Emission Spectra

1. When electrons in an atom absorb energy, they move to higher energy levels.
2. These excited states are unstable, so electrons eventually return to lower energy levels, emitting photons with specific energies.
3. This produces the line emission spectrum, a series of sharp lines that correspond to the energy differences between levels.

What is Convergence?

1. This is similar to what happens in the emission spectrum of hydrogen: as the frequency (or energy) of emitted photons increases, the spectral lines get closer together.
2. This phenomenon is called convergence. At the highest frequencies, the lines merge into a continuum, marking the limit of convergence.
3. The limit of convergence corresponds to the energy needed to completely remove an electron from the atom, also known as the ionization energy.

Connecting Convergence to Ionization Energy

The energy of a photon can be calculated using the equation:

$$E=h\cdot f$$

Where:

• $E$ = energy of the photon (in joules, J)
• $h=6.63\times {10}^{-34}$ Js (Planck's constant)
• $f$ = frequency of the radiation (in hertz, Hz, or $s^{-1}$)

The relationship between frequency ($f$) and wavelength ($\lambda$) is given by:

$$c=\lambda \cdot f$$

Where:

• $c=3.00\times {10}^8$ m/s (speed of light in a vacuum)
• $\lambda$ = wavelength (in meters)

By combining these equations, you can calculate the ionization energy of an atom if the wavelength at the convergence limit is known:

$$E=\frac{h\cdot c}{\lambda }$$

Trends in Ionization Energy

Understanding periodic trends in $IE$ helps explain the reactivity of elements.

General Trends Across Periods and Down Groups

1. Across a Period (Left to Right):
   • Trend: Ionization energy increases.
   • Reason:
     • As you move across a period, the number of protons in the nucleus increases, strengthening the nuclear charge.
     • This pulls the outermost electrons closer, making them harder to remove. Shielding by inner electrons remains relatively constant.
2. Down a Group (Top to Bottom):
   • Trend: Ionization energy decreases.
   • Reason:
     • The number of energy levels increases, placing the outermost electrons farther from the nucleus.
     • This increases electron shielding, reducing the effective nuclear charge experienced by the valence electrons.

Discontinuities in Ionization Energy

While general trends are consistent, exceptions arise due to electron configurations:

1. Between Groups 2 and 3 (e.g., Be vs. B):
   • The electron removed from boron is in the 2p sublevel, which is higher in energy and shielded by the 2s electrons.
   • This makes it easier to remove, resulting in a lower $IE$ than beryllium.
2. Between Groups 15 and 16 (e.g., N vs. O):
   • Nitrogen has a half-filled 2p sublevel, which is particularly stable.
   • In contrast, oxygen has a paired electron in the 2p sublevel, leading to increased electron-electron repulsion.
   • This makes it easier to remove an electron from oxygen, resulting in a lower $IE$.

Reflection and Connections