Answer:
The correct option is: A. 9.57 × 10⁻⁸ m
Explanation:
Given: First molar ionization energy of chlorine (Cl) = 1.25 × 10³ kJ/mol
Since, 1 kJ = 10³ J
∴ First molar ionization energy of chlorine (Cl) = 1.25 × 10³ kJ/mol = 1.25 × 10³ × 10³ J/mol = 1.25 × 10⁶ J/mol
Now, for a single Cl atom,
the first ionization energy of a Cl atom: [tex]E (J) = \frac{First\: molar\: ionization\: energy (J/mol)}{Avogadro\: constant (N_{A})}[/tex]
[tex]As\: we\: know,\: Avogadro\: constant: \: N_{A} = 6.022 \times 10^{23} mol^{-1}[/tex]
[tex]\therefore E = \frac{1.25\times 10^{6} J/mol}{6.022 \times 10^{23} mol^{-1}} = 2.076\times 10^{-18} J[/tex]
Now, to find the wavelength of light absorbed to ionize the Cl atom, we use the Planck equation:
[tex]E = h\nu =\frac{hc}{\lambda}[/tex]
[tex]Here, c:\: speed\: of\: light = 3 \times 10^{8}\: m/s[/tex]
[tex]h:\: Planck\: constant = 6.626\times 10^{-34}\: J.s\\[/tex]
[tex]\nu: frequency\: of\: light[/tex]
[tex]\lambda:\: wavelength\: of\: light = ?[/tex]
Therefore, the wavelength of light (λ) that can ionize the Cl atom: [tex]\lambda = \frac{hc}{E}[/tex]
[tex]\therefore \lambda = \frac{(6.626\times 10^{-34}\: J.s)\times 3 \times 10^{8}\: m/s}{2.076\times 10^{-18} J} = 9.575 \times 10^{-8}\: m[/tex]
Therefore, the wavelength of light (λ) required to ionize a chlorine atom = 9.57 × 10⁻⁸ m
The wavelength of the photon is 9.57x10–8 m.
The energy of the photon is obtained from;
E = 1.25 x 10^6J/6.02 x 10^23
E = 2.08 x 10^-18 J
Using the relation;
E = hc/λ
h = Plank's constant = 6.6 x 10^-34 Js
c = speed of light = 3 x 10^8 m/s
λ = wavelength = ?
λ = hc/E
λ = 6.6 x 10^-34 × 3 x 10^8 /2.08 x 10^-18
λ = 9.57x10–8 m
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