Question

The ionization energy of sodium in \(kJ \;mol^{−1}\). If electromagnetic radiation of wavelength 242 nm is just sufficient to ionize sodium atom is ______.

Answer 1

Correct Answer: 494

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 \( 494 \, \text{kJ/mol} \).

Answer 2

\[ E = \frac{1240}{\lambda (\text{nm})} \, \text{eV} \]
\[ E = \frac{1240}{242} \, \text{eV} \]
\[ E = 5.12 \, \text{eV} \]
\[ E = 5.12 \times 1.6 \times 10^{-19} \, \text{J/atom} \]
\[ E = 8.198 \times 10^{-19} \, \text{J/atom} \]
\[ E = 494 \, \text{kJ/mol} \]