The wave function for a quantum mechanical particle in a one-dimensional box of length a is given by $$\psi = A\sin \frac{{\pi x}}{a}.$$   The value of A for a box of length 200 nm is

A. 99.7 × 10^-12 m B. 199.4 × 10^-12 m C. 199.4 × 10^-18 m D. 99 × 10^-6 m

A. $$\exp \left( { - \frac{{h\nu }}{{{K_B}T}}} \right)$$ B. $${\left[ {1 - \exp \left( { - \frac{{h\nu }}{{{K_B}T}}} \right)} \right]^{ - 1}}$$ C. $$\exp \left( { - \frac{{h\nu }}{{{K_B}T}}} \right){\left[ {1 - \exp \left( { - \frac{{h\nu }}{{{K_B}T}}} \right)} \right]^{ - 1}}$$ D. $$\exp \left( { - \frac{{h\nu }}{{2{K_B}T}}} \right){\left[ {1 - \exp \left( { - \frac{{h\nu }}{{{K_B}T}}} \right)} \right]^{ - 1}}$$

A. 4 × 10⁴ (nm)² B. 10$$\sqrt 2 $$ (nm)^1/2 C. $$\sqrt 2 $$ /10 (nm)^-1/2 D. 0.1 (nm)^-1/2

A. $$\Delta \varepsilon _n^{\left( 1 \right)} = \gamma $$ B. $$\Delta \varepsilon _n^{\left( 1 \right)} = {\gamma ^2}$$ C. $$\Delta \varepsilon _n^{\left( 1 \right)} = {\gamma ^{ - 1}}$$ D. $$\Delta \varepsilon _n^{\left( 1 \right)} = 0$$