The expectation value of the z coordinate, (z), in the ground state of the hydrogen atom (wave function: $${\psi _{100}}\left( r \right) = A{e^{ - \frac{r}{{{a_0}}}}},$$    where A is the normalization constant and $${a_0}$$ is the Bohr radius), is

A particle is placed in a one-dimensional box of size L along the X-axis, (0 < x < L). Which of the following is true?

If the probability that x lies between x and x + dx is P(x) dx = ae^-ax dx, where 0 < x < $$\infty $$ , a > 0, then the probability that x lies between x₁ and x₂ (x₂ > x₁) is

A Michelson interferometer is illuminated with monochromatic light. When one of the mirrors is moved through a distance of 25.3 μm, 92 fringes pass through the cross-wire. The wavelength of the monochromatic light is

An electron is in a statewith spin wavefunction \[{\phi _s} = \left[ {\begin{array}{*{20}{c}} {\frac{{\sqrt 3 }}{2}} \\ {\frac{1}{2}} \end{array}} \right]\]  in the s_z representation. What is the probability of, finding the z-component of its spin along the $$ - {\bf{\hat Z}}$$  direction?