The amount of energy necessary to remove an electron from an atom is a quantity called the ionization energy, Ei. This energy can be measured by a technique called photoelectron spectroscopy, in which light of wavelength l is directed at an atom, causing an electron to be ejected. The kinetic energy of the ejected electron (Ek) is measured by determining its veloc-ity, v (Ek = mv2/2), and Ei is then calculated using the conservation of energy principle. That is, the energy of the incident light equals Ei plus Ek. What is the ionization energy of selenium atoms in kilojoules per mole if light with l = 48.2 nm produces electrons with a velocity of 2.371 * 106 m/s? The mass, m, of an electron is 9.109 * 10-31 kg.

Verified step by step guidance

1. Calculate the energy of the incident light using the formula $E = \frac{hc}{\lambda}$, where $h$ is Planck's constant ($6.626 \times 10^{-34}$ J s), $c$ is the speed of light ($3.00 \times 10^8$ m/s), and $\lambda$ is the wavelength of the light in meters.
2. Convert the wavelength from nanometers to meters by multiplying by $10^{-9}$.
3. Calculate the kinetic energy of the ejected electron using the formula $E_k = \frac{1}{2}mv^2$, where $m$ is the mass of the electron ($9.109 \times 10^{-31}$ kg) and $v$ is the velocity of the electron.
4. Apply the conservation of energy principle to find the ionization energy: $E_i = E - E_k$, where $E$ is the energy of the incident light and $E_k$ is the kinetic energy of the ejected electron.
5. Convert the ionization energy from joules to kilojoules per mole by multiplying by Avogadro's number ($6.022 \times 10^{23}$ mol$^{-1}$) and then dividing by $1000$ to convert joules to kilojoules.

Key Concepts

Ionization Energy

Ionization energy (Ei) is the amount of energy required to remove an electron from an atom in its gaseous state. It is a crucial concept in understanding the reactivity and stability of elements, as it reflects how tightly an atom holds onto its electrons. Higher ionization energies indicate that an atom is less likely to lose an electron, while lower values suggest a greater tendency to ionize.

Photoelectron Spectroscopy

Photoelectron spectroscopy is an experimental technique used to measure the ionization energy of atoms. In this method, photons of light are directed at an atom, causing the ejection of electrons. By measuring the kinetic energy of these ejected electrons, researchers can determine the energy required to remove an electron, thus providing insights into the electronic structure of the atom.

Conservation of Energy

The conservation of energy principle states that energy cannot be created or destroyed, only transformed from one form to another. In the context of ionization energy, this principle is applied to relate the energy of the incoming photons to the energy required to ionize the atom and the kinetic energy of the ejected electron. This relationship allows for the calculation of ionization energy using the equation: Energy of light = Ionization energy + Kinetic energy of electron.