Solution:

To find the electron density in doped silicon, we need to understand the concept of doping and its effect on the number of electron and hole densities.

Doping:
Doping is the process of intentionally adding impurities to a semiconductor material to alter its electrical properties. In this case, indium is being used as the dopant.

Number Density of Electron and Holes in Pure Silicon:
Given that the number density of electrons and holes in pure silicon at 27°C is equal and has a value of 2.0×10^16 m^-3.

Effect of Doping:
When indium is doped into silicon, it acts as a donor impurity. Indium has five valence electrons compared to the four valence electrons of silicon. So, when indium atoms replace silicon atoms in the crystal lattice, an extra electron is freed up.

Increased Hole Density:
The freed-up electron from the indium atom becomes a conduction electron, while the indium atom itself creates a hole. Therefore, the doping of indium increases the hole density in the silicon crystal.

Given that the hole density increases to 4.5×10^22 m^-3, we can conclude that the number of holes in doped silicon is 4.5×10^22 m^-3.

Electron Density in Doped Silicon:
Since the number of electrons and holes in a doped semiconductor must be equal to maintain charge neutrality, the electron density in doped silicon will also be 4.5×10^22 m^-3.

Therefore, the electron density in doped silicon is 4.5×10^22 m^-3.

In summary:
- The number density of electron and holes in pure silicon at 27°C is 2.0×10^16 m^-3.
- Doping with indium increases the hole density to 4.5×10^22 m^-3.
- The number of electrons in doped silicon is equal to the hole density, so the electron density is also 4.5×10^22 m^-3.

The relationship of the doped semiconductor is given by 
nhne=ni^2
Where  ni=2.0×10^16   nh=4.6×10^22. So we have,
ne=ni^2/nh. =(2.0×10^16)^2/4.6×10^22. =8.6×10^9