The ionization energy of sodium in \(kJ \;mol^{−1}\). If electromagnetic radiation of wavelength 242 nm is just sufficient to ionize sodium atom is ______.
Correct Answer: 494
Approach Solution - 1
Given Formula:
The energy of a photon is given by the formula:
\[ E = \frac{1240}{\lambda (\text{nm})} \, \text{eV} \]
Step 1: Substitute the wavelength:
Substitute the wavelength into the equation:
\[ E = \frac{1240}{242} \, \text{eV} \]
Step 2: Simplify to find the energy in eV:
After performing the calculation:
\[ E = 5.12 \, \text{eV} \]
Step 3: Convert to Joules per atom:
To convert from eV to Joules, multiply by \( 1.6 \times 10^{-19} \, \text{J/eV} \):
\[ 5.12 \times 1.6 \times 10^{-19} = 8.198 \times 10^{-19} \, \text{J/atom} \]
Step 4: Convert to kJ/mol:
To convert from Joules per atom to kJ per mole, multiply by Avogadro's number (\( 6.022 \times 10^{23} \)) and divide by 1000:
\[ 8.198 \times 10^{-19} \times 6.022 \times 10^{23} = 494 \, \text{kJ/mol} \]
Final Answer:
The energy is \( 494 \, \text{kJ/mol} \).
Approach Solution -2
\[ E = \frac{1240}{\lambda (\text{nm})} \, \text{eV} \]
\[ E = \frac{1240}{242} \, \text{eV} \]
\[ E = 5.12 \, \text{eV} \]
\[ E = 5.12 \times 1.6 \times 10^{-19} \, \text{J/atom} \]
\[ E = 8.198 \times 10^{-19} \, \text{J/atom} \]
\[ E = 494 \, \text{kJ/mol} \]
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