51. The energy $$E\left( {\overrightarrow {\bf{k}} } \right)$$ of electrons of wave vector $$\overrightarrow {\bf{k}} $$ in a solid is given by $$E\left( {\overrightarrow {\bf{k}} } \right) = A{k^2} + B{k^4},$$ where A and B are constants. The effective mass of the electron at $$\left| {\overrightarrow {\bf{k}} } \right| = {k_0}$$ is
52. The effective density of states at the conduction band edge of Ge is 1.04 × 1019 cm-3 at room temperature (300 K). Ge has an optical band gap of 0.66 eV. The intrinsic carrier concentration (in cm-3) in Ge at room temperature (300 K) is approximately
53. Which one of the following statements is true?
54. A linear diatomic lattice of lattice constant a with masses M and m (M > m) are coupled by a force constant C. The dispersion relation is given by $${\omega ^2} = C\left( {\frac{{M + m}}{{Mm}}} \right) \pm {\left[ {{C^2}{{\left( {\frac{{m + m}}{{Mm}}} \right)}^2} - \frac{{4{C^2}}}{{Mm}}{{\sin }^2}\frac{{ka}}{2}} \right]^{\frac{1}{2}}}$$
Which one of the following statements is incorrect?
Which one of the following statements is incorrect?