Question

Use data from Table 3.3 to give an upper bound on thewavelengthsof light that are capable of dissociating amolecule of Cl-F.

Short answer

The wavelength of light that is capable of dissociating a molecule of Cl-F is

.${\text{7.882×10}}^{\text{-28}}\text{m}$

Step-by-step solution

Step 1:Wavelength of light

The Greek letter lambda ($\text{λ}$ ) is used to represent wavelength.As we know, the wavelength is defined as the distance between one “wave's crest or trough” and the following wave's crest or trough.

Given information

The given data has values as follows:

• h =$6.626\times {10}^{-34}\text{Js}$ (Planck’s constant)

• c = $\text{2.99}\times {\text{10}}^{\text{8}}{\text{ms}}^{\text{-1}}$ (Speed of light)

• E= 252 kJ mol^-1(Bond dissociation energy of Cl-F bond)

Wavelength of light for dissociating a molecule

From table 3.3, the bond dissociation energy of a typical Cl-F bond is approximately 252 kJ/mol.

The energy of radiation is related to its wavelength as given by the equation.

$\begin{array}{c}\text{E=}\frac{\text{hc}}{\text{λ}}\\ \text{or,λ=}\frac{\text{hc}}{\text{E}}\end{array}$

The known values are substituted.

$\begin{array}{l}\text{λ=}\frac{{\text{6.626×10}}^{\text{34}}{\text{×2.99879×10}}^{\text{8}}}{\text{252}}\\ {\text{λ=7.882×10}}^{\text{-28}}\text{m}\end{array}$.

Therefore, wavelength of light that are capable of dissociating a molecule of Cl-F is ${\mathbf{\text{7.882×10}}}^{\mathbf{\text{-28}}}\mathbf{\text{m}}$