Answer:
The value of the function is [tex]q__{t }} = 1.878 *10^{35}[/tex]
Explanation:
From the question we are told that
The temperature is [tex]T = 1000 \ K[/tex]
The volume is [tex]V = 1 m^3[/tex]
Generally the transnational partition function is mathematically represented as
[tex]q__{t }} = [\frac{2 * \pi * m * k * T }{ N_a * h} ]^{\frac{3}{2} } * V[/tex]
Where m is the molar mass of oxygen with a constant value of [tex]m = 32 *10^{-3} \ kg/mol[/tex]
k is the Boltzmann constant with a value of [tex]k = 1.38 *10^{-23 } \ J/K[/tex]
[tex]N_a[/tex] is the Avogadro Number with a constant value of [tex]N_a = 6.022 *10^{23} \ atoms[/tex]
h is the Planck's constant with value [tex]h = 6.626 *10^{-34 } \ J\cdot s[/tex]
Substituting values
[tex]q__{t }} = [\frac{2 * 3.142 * 32*10^{-3} * 1.38 *10^{-23} * 1000 }{ 6.022 *10^{23} * [6.626 *10^{-34}] ^2 }]^{\frac{3}{2} } * 1[/tex]
[tex]q__{t }} = 1.878 *10^{35}[/tex]
