Ionization Energy and Wavelength of Radiation for Sodium Atom

Ionization energy is the energy required to remove an electron from an atom or ion in its ground state. In the case of the sodium atom, the ionization energy is given as 4.946 x 10^2 kJ/mol.

Ionization Energy:
The ionization energy can be calculated using the equation:
Ionization energy = (h * c) / λ
where h is the Planck's constant (6.626 x 10^-34 J.s), c is the speed of light (3.00 x 10^8 m/s), and λ is the wavelength of the radiation.

Calculating Wavelength:
To find the wavelength of the radiation that is sufficient to ionize the sodium atom, we rearrange the equation:
λ = (h * c) / Ionization energy

Substituting the given values:
λ = (6.626 x 10^-34 J.s * 3.00 x 10^8 m/s) / (4.946 x 10^2 kJ/mol * 1000 J/kJ)
Simplifying the equation:
λ = (6.626 x 10^-34 J.s * 3.00 x 10^8 m/s) / (4.946 x 10^5 J/mol)

Converting Units:
Since the units of J.s and m/s cancel each other out, we are left with the unit of mol in the denominator. We need to convert mol to atoms using Avogadro's number (6.022 x 10^23 atoms/mol), so that the final answer is in terms of atoms.

λ = (6.626 x 10^-34 J.s * 3.00 x 10^8 m/s) / (4.946 x 10^5 J/mol * 6.022 x 10^23 atoms/mol)

Final Calculation:
By performing the calculation, we get:
λ = 2.54 x 10^-7 m

Conclusion:
The wavelength of radiation sufficient to ionize a sodium atom is approximately 2.54 x 10^-7 meters.