Homework Help is Here – Start Your Trial Now!
Science
Advanced Physics
· Consider the recombination of hydrogen ions (and the ionization of hydrogen atoms) H* +e" ++ H or H – H* - e¯ = 0. Suppose that at some very low temperature, we start with a density no of pure hydrogen atoms in some fixed volume. The temperature is then raised to temperature T, at which some ionization may occur. Let K„(T) be the equilibrium constant for this reaction, and let IE noKn(T).

· Consider the recombination of hydrogen ions (and the ionization of hydrogen atoms) H* +e" ++ H or H – H* - e¯ = 0. Suppose that at some very low temperature, we start with a density no of pure hydrogen atoms in some fixed volume. The temperature is then raised to temperature T, at which some ionization may occur. Let K„(T) be the equilibrium constant for this reaction, and let IE noKn(T).

icon
Related questions
Question

Im stuck on the following Thermodynamics problem!

. Consider the recombination of hydrogen ions (and the ionization of hydrogen atoms) H+ +e + H or H – Ht - e = 0. Suppose that at some very low temperature, we start with a density no of pure hydrogen atoms in some fixed volume. The temperature is then raised to temperature T, at which some ionization may occur. Let K,(T) be the equilibrium constant for this reaction, and let * = noKn(T). (a) Show that if r > 1, only one in every vI of the H atoms is ionized. (b) Show that if r <1, the gas is almost entirely ionized. (c) Show that if r = 1, ~62% of the H atoms are ionized. (d) Treat the H atoms, and the H+ and e- ions, as classical "monatomic" ideal gases, but let the H atoms have a constant negative potential energy -Eg (the binding energy). Calculate K, (T) in terms of En; the masses of H, H+, and e-; T; and ho, the constant that describes the counting of states in classical phase space. (e) Explain why your answer to (d) shows that classical physics cannot really be valid here. (f) Ignore (e) and plug in numerical values to get K„(T) at T = 104 K, T = 105 K, and T = 106 K. Use Eo = 13.6 eV and ho = h (Planck's constant). (g) Calculate the fraction of ionized H atoms at T = 10' K, T = 105 K, and T = 10 K. Use no = 1023 /liter.
Transcribed Image Text:. Consider the recombination of hydrogen ions (and the ionization of hydrogen atoms) H+ +e + H or H – Ht - e = 0. Suppose that at some very low temperature, we start with a density no of pure hydrogen atoms in some fixed volume. The temperature is then raised to temperature T, at which some ionization may occur. Let K,(T) be the equilibrium constant for this reaction, and let * = noKn(T). (a) Show that if r > 1, only one in every vI of the H atoms is ionized. (b) Show that if r <1, the gas is almost entirely ionized. (c) Show that if r = 1, ~62% of the H atoms are ionized. (d) Treat the H atoms, and the H+ and e- ions, as classical "monatomic" ideal gases, but let the H atoms have a constant negative potential energy -Eg (the binding energy). Calculate K, (T) in terms of En; the masses of H, H+, and e-; T; and ho, the constant that describes the counting of states in classical phase space. (e) Explain why your answer to (d) shows that classical physics cannot really be valid here. (f) Ignore (e) and plug in numerical values to get K„(T) at T = 104 K, T = 105 K, and T = 106 K. Use Eo = 13.6 eV and ho = h (Planck's constant). (g) Calculate the fraction of ionized H atoms at T = 10' K, T = 105 K, and T = 10 K. Use no = 1023 /liter.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer