What is the maximum number of Cs+ ions that can be produced per joule of energy absorbed by a sample of gaseous Cs atoms?
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To determine the maximum number of Cs+ ions that can be produced per joule of energy absorbed by a sample of gaseous Cs atoms, we need to consider the ionization energy of the Cs atoms.
1. Find the ionization energy of Cs: Ionization energy is the minimum energy required to remove an electron from an atom or ion. Look up the ionization energy of Cs. Based on the periodic table, the ionization energy of Cs is approximately 3.89 electron volts (eV).
2. Convert the ionization energy to joules: One electron volt is equal to 1.602 x 10^-19 joules. Therefore, the ionization energy in joules can be calculated by multiplying the ionization energy in eV by the conversion factor. In this case, the ionization energy in joules would be approximately 6.23 x 10^-19 joules.
3. Calculate the maximum number of Cs+ ions produced per joule: By dividing 1 joule by the ionization energy in joules, we get the maximum number of Cs+ ions produced per joule of energy absorbed by the Cs atoms. In this case, it would be:
1 joule / 6.23 x 10^-19 joules ≈ 1.60 x 10^18 Cs+ ions per joule
So, the maximum number of Cs+ ions produced per joule of energy absorbed by a sample of gaseous Cs atoms is approximately 1.60 x 10^18 Cs+ ions per joule.
To determine the maximum number of Cs+ ions produced per joule of energy absorbed by a sample of gaseous Cs atoms, we need to use the concept of ionization energy.
Ionization energy is the amount of energy required to remove an electron from an atom or ion in its ground state. For the formation of Cs+ ions, we need to remove one electron from a Cs atom.
The energy absorbed per mole of Cs atoms is known as the molar ionization energy (IE). The molar ionization energy is reported in units of joules per mole (J/mol).
The maximum number of Cs+ ions that can be produced per joule of energy absorbed by a sample of gaseous Cs atoms can be calculated using the Avogadro's number (6.022 x 10^23) and the molar ionization energy.
Here are the steps to calculate the maximum number of Cs+ ions:
Step 1: Look up the molar ionization energy (IE) for Cs. Let's assume it is 382.73 kJ/mol or 382730 J/mol.
Step 2: Convert the molar ionization energy to joules per atom:
IE (J/atom) = IE (J/mol) / Avogadro's number
IE (J/atom) = 382730 J/mol / 6.022 x 10^23
Step 3: Calculate the maximum number of Cs+ ions produced per joule of energy absorbed:
Number of Cs+ ions = 1 / IE (J/atom)
Let's calculate the number of Cs+ ions per joule using the assumed value for molar ionization energy:
IE (J/atom) = 382730 J/mol / 6.022 x 10^23
≈ 6.356 x 10^-19 J/atom
Number of Cs+ ions per joule = 1 / 6.356 x 10^-19 J/atom
≈ 1.572 x 10^18 Cs+ ions
Therefore, the maximum number of Cs+ ions that can be produced per joule of energy absorbed by a sample of gaseous Cs atoms is approximately 1.572 x 10^18 Cs+ ions.
Please note that the molar ionization energy value may vary based on different sources, so make sure to use the correct value when performing calculations.