A piece of metal can be considered as a reservoir of...

A piece of metal can be considered as a reservoir of electrons; the work function (energy to remove an electron from the metal) is 4 eV . Considering only the is orbital (which can be occupied by zero, one, or two electrons) and knowing that the hydrogen atom has an ionization energy of 13.6 eV and an electron affinity of 0.6 eV , determine for atomic hydrogen in chemical equilibrium at $T=300 \mathrm{~K}$ in the vicinity of a metal the probabilities of finding $\mathrm{H}^{+}, \mathrm{H}^0$ and $\mathrm{H}^{-}$. Give only one significant figure. What value of the work function would give equal probabilities to $\mathrm{H}^0$ and $\mathrm{H}^{-}$?

A piece of metal can be considered as a reservoir of electrons; the work function (energy to remove an electron from the metal) is 4 eV . Considering only the is orbital (which can be occupied by zero, one, or two electrons) and knowing that the hydrogen atom has an ionization energy of 13.6 eV and an electron affinity of 0.6 eV , determine for atomic hydrogen in chemical equilibrium at $T=300 \mathrm{~K}$ in the vicinity of a metal the probabilities of finding $\mathrm{H}^{+}, \mathrm{H}^0$ and $\mathrm{H}^{-}$. Give only one significant figure.

What value of the work function would give equal probabilities to $\mathrm{H}^0$ and $\mathrm{H}^{-}$?

Key Concepts

Work Function

The work function is the minimum energy required to remove an electron from a metallic surface. In contexts involving electron transfer between a metal and nearby atoms or molecules, it sets the electron chemical potential and thus plays a critical role in determining the relative populations of different ionization states in chemical equilibrium.

Ionization Energy

Ionization energy is the amount of energy needed to remove an electron from a neutral atom, leading to the formation of a positive ion. This parameter is essential when considering equilibrium among different charged states, as it directly affects the energy balance and the population of species like H+ in a system.

Electron Affinity

Electron affinity is the energy change that occurs when an electron is added to a neutral atom, forming a negative ion. It determines the stability of the anionic form in a chemical equilibrium involving electron transfer, where it competes with the work function and ionization energy to set the relative likelihood of the anion.

Boltzmann Factor

The Boltzmann factor is a term in statistical mechanics that gives the relative probability of a system being in a state with a particular energy. It is expressed as an exponential function of the negative energy difference divided by kT, and it is used to calculate the equilibrium distribution among different species based on their energy differences.

Chemical Equilibrium in Electron Transfer

Chemical equilibrium in electron transfer involves the balance between electron attachment and detachment processes between a reservoir (such as a metal) and atomic or molecular species. In this context, the relative populations of species like H+, H0, and H– are determined by the interplay of the work function, ionization energy, electron affinity, and temperature, with the Boltzmann factor providing the statistical framework for these distributions.

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