Question 10 of 62intermediate🔧 ApplyNumerical2 marks

Electromagnetic radiation of wavelength 242 nm is just sufficient to ionise the sodium atom. Calculate the ionisation energy of sodium in kJ mol⁻¹.

Correct Answer

494.6 kJ mol⁻¹

Exercise: EXERCISES | Q: 2.10 | (Page 41)
For More Understanding

Explanation

The ionisation energy of sodium is the energy required to remove one mole of electrons from one mole of sodium atoms. Since the radiation of 242 nm is just sufficient to ionise the atom, the energy of one photon at this wavelength equals the ionisation energy of one atom. Multiplying this by Avogadro's number gives the ionisation energy per mole.

Solution Steps

  1. Step 1: Calculate the energy of one photon Using the formula E=hcλE = \frac{hc}{\lambda}:

    E=6.626×10−34 J s×3.0×108 m s−1242×10−9 m=8.214×10−19 JE = \frac{6.626 \times 10^{-34} \text{ J s} \times 3.0 \times 10^{8} \text{ m s}^{-1}}{242 \times 10^{-9} \text{ m}} = 8.214 \times 10^{-19} \text{ J}

  2. Step 2: Calculate the ionisation energy per mole Multiply the energy of one photon by Avogadro's number (6.022×1023 mol−16.022 \times 10^{23} \text{ mol}^{-1}):

    Emol=8.214×10−19 J×6.022×1023 mol−1=4.946×105 J mol−1E_{\text{mol}} = 8.214 \times 10^{-19} \text{ J} \times 6.022 \times 10^{23} \text{ mol}^{-1} = 4.946 \times 10^{5} \text{ J mol}^{-1}

  3. Step 3: Convert to kJ mol⁻¹

    Emol=4.946×105 J mol−11000=494.6 kJ mol−1E_{\text{mol}} = \frac{4.946 \times 10^{5} \text{ J mol}^{-1}}{1000} = 494.6 \text{ kJ mol}^{-1}
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