The first excited state of helium (He) is 159,850 cm-1 above the ground state. The first excited state of fluorine (F) is 404 cm-1 above the ground state. If we define the fraction of the atoms in the first excited state (fes) as LaTeX: f_{\text{fes}}[\text{He or F}]f fes [ He or F ], which of the following statements is TRUE at a temperature of 1000 K?

a) ƒfes [F] = 0
b) ƒfes [F] = 1
c) ƒfes [H] = 1
d) ƒfes [F] < ƒfes [H]
e) ƒfes [F] > ƒfes [H]

Answer :

Answer:

correct option is C i.e  F_{fes} [F] > F_{fes} [He]

Explanation:

Given data:

excited state of helium is given as 159,850 cm^{-1}

In terms of joule  = [tex]6.626\times 10^{-34} \times 3\times 10^{10} \times 159,850[/tex]

                             [tex]= 3.177\times 10^{-18} J[/tex]

First excited state of fluorine is [tex]404 cm^{-1}[/tex]

in terms of joule is [tex]= 6.626\times 10^{-34} \times 3\times 10^{10} \times 404[/tex]

                             [tex]= 8.030\times 10^{-21} J[/tex]

so, [tex]F_{fes} [He] = e^{- \frac {3.177\times 10^{-18}}{1.38\times 10^{-23}\times 1000}[/tex]    

where   T =1000 k

[tex]F_{fes} [He] = 0[/tex]

[tex]F_{fes} [He] = e^{- \frac {8.030\times 10^{-21}}{1.38\times 10^{-23}\times 1000}[/tex]    

where   T = 1000 k

[tex]F_{fes} [F] = 0.55[/tex]

Therefore .  [tex]F_{fes} [F] > F_{fes} [He][/tex]

correct option is C

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