Respuesta :
Answer:
The answer to the question is
The energy (in kJ/mol) for vacancy formation assuming that the density of the metal remains the same over this temperature range is 3.41165×10⁻²² kJ/mol
Explanation:
To solve the question, we note that the Boltzmann equation for vibrational states is
[tex]\frac{N_{1} }{N_0} =e^{\frac{-dE}{kT} }[/tex] Where
N₀ = Population of the lower energy state
N₁ = Population of the upper energy state
ΔE = dE = The energy difference between the two states
k = the Boltzmann constant and
T = Kelvin temperature
Therefore we have
[tex]6N_e ^{(\frac{-Q_v }{k(1070)})} = N_e ^{(\frac{-Q_v }{k(1160)}) }\\[/tex]
From which
[tex]6 = \frac{N_e ^{(\frac{-Q_v }{k(1160)}) }}{N_e ^{(\frac{-Q_v }{k(1070)})}}\\[/tex]
[tex]6 = \frac{e ^{(\frac{-Q_v }{k(1160)}) }}{e ^{(\frac{-Q_v }{k(1070)})}}\\[/tex]
[tex]6 = e ^{{(\frac{-Q_v }{k(1160)}) }{{+(\frac{Q_v }{k(1070)})}}}[/tex]
[tex]ln(6) = {{(\frac{-Q_v }{k(1160)}) }{{+(\frac{Q_v }{k(1070)})}}}[/tex]
[tex]Q_v =\frac{ ln(6) }{{(\frac{1 }{k(1160)}) }{{+(\frac{1 }{k(1070)})}}}[/tex]
Therefore
[tex]Q_v[/tex] = 3.41165×10⁻²² kJ/mol
