Question

Calculate the Hall coefficient for potassium which has a bcc structure with a lattice
constant of 0.538 nm.

Answer 1

Answer on Question #61902, Physics / Solid State Physics

Calculate the Hall coefficient for potassium which has a bcc structure with a lattice constant of 0.538 nm.

Solution:

$$R _ {h} = \frac {1}{e n}$$

Where, n is concentration of electrons; e is electron charge.

$$\frac {\text {atomic weight}}{\rho} \times 1 0 ^ {- 6} = a ^ {3} \frac {N _ {a}}{n}$$ $$n = \rho a ^ {3} \frac {N _ {a}}{\text {atomic weight} \times 1 0 ^ {- 6}}$$

Then,

$$R _ {h} = \frac {\text {atomic weight} \times 1 0 ^ {- 6}}{e \rho a ^ {3} N _ {a}}$$

Where, atomic weight for potassium (39,0983 g/moll), $\rho$ density (0,856 g/cm³), a is a lattice constant (5,38*10⁻⁸ cm), $N_{A} = 6,022 \times 10^{23} \mathrm{~moll}^{-1}$

$$R _ {h} = \frac {3 9 , 0 9 8 3 \mathrm {g / m o l l} \times 1 0 ^ {- 6}}{1 . 6 \cdot 1 0 ^ {- 1 9} \mathrm {C} \times 0 , 8 5 6 \mathrm {g / c m} ^ {3} \times (5 , 3 8 \cdot 1 0 ^ {- 8} \mathrm {c m}) ^ {3} \times 6 , 0 2 2 \cdot 1 0 ^ {2 3} \mathrm {m o l l} ^ {- 1}} = 3. 4 \cdot 1 0 ^ {1 2} C ^ {- 1}$$

Answer: $3.4 \cdot 10^{12} C^{-1}$

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