Final answer:
To calculate the electron contribution to specific heat of magnesium, we use the equation Cv = 3nR and rearrange it to solve for n. Given Cv = 6.161 J/K and KT = 50 K, we calculate n and multiply it by Avogadro's number to find the number of electrons. Finally, we use the equation Ce = Cv / number of electrons to calculate the electron contribution, which is 0.123 J.
Step-by-step explanation:
To calculate the electron contribution to the specific heat of magnesium, we can use the equation Cv = 3nR, where Cv is the molar specific heat capacity, n is the number of moles, and R is the gas constant. We can rearrange this equation to solve for n: n = Cv / (3R). Given Cv = 6.161 J/K and KT = 50 K, we can calculate n:
n = (6.161 J/K) / (3(8.314 J/mol·K)(50 K)) = 0.0117 mol
Since magnesium has 6.022 × 10^23 electrons per mole, we can multiply n by Avogadro's number to find the number of electrons: (0.0117 mol)(6.022 × 10^23 electrons/mol) = 7.05 × 10^21 electrons
Finally, the electron contribution to specific heat can be calculated using the equation Ce = Cv / (number of electrons): Ce = 6.161 J/K / (7.05 × 10^21 electrons) = 0.123 J