Question

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 1

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

Step-by-step explanation:

Given data:

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

In terms of joule =
`6.626* 10^(-34) * 3* 10^(10) * 159,850`

`= 3.177* 10^(-18) J`

First excited state of fluorine is
`404 cm^(-1)`

in terms of joule is
`= 6.626* 10^(-34) * 3* 10^(10) * 404`

`= 8.030* 10^(-21) J`

so,
`F_(fes) [He] = e^{- \frac {3.177* 10^(-18)}{1.38* 10^(-23)* 1000}`

where T =1000 k

`F_(fes) [He] = 0`

`F_(fes) [He] = e^{- \frac {8.030* 10^(-21)}{1.38* 10^(-23)* 1000}`

where T = 1000 k

`F_(fes) [F] = 0.55`

Therefore .
`F_(fes) [F] > F_(fes) [He]`

correct option is C