Question

Calculate the wavelength of light required to break the bond between two chlorine atoms in a chlorine molecule. The \[Cl-Cl\] bond energy is \[243\,kJmo{{l}^{-1}}.(h=6.6\times {{10}^{-34}}\,Js;c=3\times {{10}^{8}}\,m{{s}^{-1}}\], Avogadro Number \[=6.023\times {{10}^{23}}\,mol{{e}^{-1}}).\]
A. \[4.11\times {{10}^{-7}}m\]
B. \[4.91\times {{10}^{-6}}m\]
C. \[8.81\times {{10}^{-31}}m\]
D. \[6.26\times {{10}^{-21}}m\]

Answer 1

Hint: The wavelength is the distance between two wave crests, which is the same as the distance between two troughs. The number of waves that pass through a given point in one second is called the frequency, measured in units of cycles per second called Hertz.

Complete step by step answer:
The energy required to break \[Cl-Cl\] bond
The energy required to dissociate a \[Cl-Cl\] bond in a chlorine (\[C{{l}_{2}}\]) molecule \[=243000\,Jmo{{l}^{-1}}/6.023\times 10^{23}mo{{l}^{-1}}\,=4.0\,\times {{10}^{-19}}J\]
\[=\dfrac{Bond \,Energy\, Per\, Mole}{Avogadro's \,Number}\]
Let the wavelength of the photon required to break one \[Cl-Cl\] bond be \[\lambda \] .
\[\Rightarrow \lambda =\dfrac{hc}{E}=\dfrac{6.6\times {{10}^{-34}}\times 3\times {{10}^{8}}\times 6.023\times {{10}^{23}}}{243\times {{10}^{3}}}\]
\[\Rightarrow \lambda =\dfrac{119.255\times {{10}^{-34}}\times {{10}^{31}}\times {{10}^{-3}}}{243}\]
\[ \Rightarrow \lambda \, = \,4.11\times {{10}^{-7}}m\]

So, the correct option is A \[4.11\times {{10}^{-7}}m\].

Additional Information:
The frequency of a wave is just the length of one complete wave cycle. ... The frequency can be estimated as the good ways from peak to peak or from box to box. Indeed, the frequency of a wave can be estimated as the good ways from a point on a wave to the relating point on the following pattern of the wave.
Frequency and recurrence are conversely related so longer waves have lower frequencies, and more limited waves have higher frequencies. In the visual framework, a light wave's frequency is for the most part connected with shading, and its sufficiency is related with brilliance.

Note:
Wavelength can be calculated using the following formula: wavelength = wave velocity/frequency. Wavelength usually is expressed in units of meters.
$f$ = (frequency)
\[c\] (velocity of light) \[=3\times {{10}^{8}}m/s\]
\[\lambda\] (Wavelength) = $\dfrac{c}{f} $