Which of the following statements is true?

Doping of a semiconductor (with small impurity atoms) generally changes the resistivity as follows.

$A$ donor atom in a semiconductor has a loosely bound electron. The orbit of this electron is considerably affected by the semiconductor material but behaves in many ways like an electron orbiting a hydrogen nucleus. Given that the electron has an effective mass of $0.07 \, m_e$,where $m_e$ is the mass of the free electron,and the space in which it moves has a permittivity of $13 \, \varepsilon_0$,then the radius of the electron's lowermost energy orbit will be close to ................. $\mathring{A}$ (take the Bohr radius of the hydrogen atom as $0.53 \mathring{A}$).

In an $N$-type $Ge$ semiconductor,the mobility of electrons is $5000 \ cm^2/V \cdot s$ and the conductivity is $5 \ mho/cm$. If the effect of holes is negligible,what is the concentration of impurity atoms?

In a $P$-type semiconductor, the acceptor level is $57 \text{ meV}$ above the valence band. What is the maximum wavelength of light (in $\mathring{A}$) required to create a hole?

$A$ pure $Si$ crystal has $4 \times 10^{28}$ atoms per $m^3$. It is doped with $1 \text{ ppm}$ concentration of antimony. The number of free electrons available will be