A certain telescope forms an image of part of a cluster of stars on a square silicon charge-coupled detector (CCD) chip 2.00 $\mathrm{cm}$ on on each side. A star field is focused on the CCD chip when it is first turned on and its temperature is $20.0^{\circ} \mathrm{C}$ . The star field contains 5342 stars scattered uniformly. To make the detector more sensitive, it is cooled to $-100^{\circ} \mathrm{C}$ . How many star images then fit onto the chip? The average coefficient of linear expansion of silicon is
$4.68 \times 10^{-6}\left(^{\circ} \mathrm{C}\right)^{-1}$ .