Respuesta :
Answer:
The difference in energy between the [tex]S_1[/tex] and [tex]T_1[/tex] states is 35.7 kJ/mol.
Explanation:
The Planck's equation :
[tex]E=\frac{hc}{\lambda} [/tex]
Where:
E = Energy of the electromagnetic radiations.
h = Planck's constant = [tex]6.626\times 10^{-34} Js[/tex]
c = speed of light = [tex]3\times 10^8 m/s[/tex]
[tex]\lambda [/tex] = Wavelength of the electromagnetic radiations.
Energy associated with [tex]T_1[/tex] transition : [tex]E_1[/tex]
Wavelength associated with [tex]T_1[/tex] transition :
[tex]\lambda _1=397 nm=397\times 10^{-9} m[/tex]
Energy associated with [tex]S_1[/tex] transition : [tex]E_2[/tex]
Wavelength associated with [tex]S_1[/tex] transition : [tex]\lambda _2=355 nm=355\times 10^{-9} m[/tex]
The difference in energy between the [tex]S_1[/tex] and [tex]T_1[/tex] states:
[tex]E=E_1-E_2=\frac{hc}{\lambda _2}-\frac{hc}{\lambda _1}[/tex]
[tex]E=hc\times (\frac{1}{\lambda _2}-\frac{1}{\lambda _1})[/tex]
[tex]E=6.626\times 10^{-34} Js \times 3\times 10^8 m/s(\frac{1}{355\times 10^{-9}m}-\frac{1}{397\times 10^{-9} m})[/tex]
[tex]E=5.92\times 10^{-20} J[/tex]
1 J = 0.001 kJ
[tex]E=5.92\times 10^{-20}\times 10^{-3} kJ=5.92\times 10^{-23} kJ[/tex]
1 mole = [tex]6.022\times 10^{-23}[/tex]
The difference in energy(kJ/mol) between the [tex]S_1[/tex] and [tex]T_1[/tex] states:
[tex]=5.92\times 10^{-23} kJ\times 6.022\times 10^{23} mol^{-1}=35.7 kJ/mol[/tex]
