Explanation:

Introduction:
Cyanobacteria are a group of photosynthetic bacteria that are capable of producing their own food through photosynthesis. They are commonly found in freshwater environments such as lakes, ponds, and rivers. When cyanobacteria are placed in purified water, several changes occur in their cells.

Effect of purified water on cyanobacteria cells:
When cyanobacteria are placed in purified water, the following changes occur in their cells:

1. Swelling: The cells of cyanobacteria will absorb water from the purified water through a process called osmosis. This leads to an increase in the volume of the cells, causing them to swell.

2. No bursting: Although the cells of cyanobacteria swell due to the absorption of water, they do not burst. This is because cyanobacteria have a rigid cell wall that provides support and prevents the cells from bursting even when they are under increased pressure.

3. Cell wall protection: The cell wall of cyanobacteria is made up of a tough, protective layer called peptidoglycan. This layer helps maintain the shape and integrity of the cell, even when it swells due to osmosis. It acts as a barrier that prevents the cell from bursting.

4. No change in shape: Despite the swelling, the overall shape of the cyanobacteria cells remains relatively unchanged. This is because the rigid cell wall prevents the cells from deforming or losing their shape.

5. No change in function: The swelling of cyanobacteria cells in purified water does not affect their normal functioning. They can continue to carry out photosynthesis and other cellular processes without any significant impairment.

Conclusion:
When cyanobacteria cells are placed in purified water, they will swell due to the absorption of water through osmosis. However, their rigid cell wall prevents them from bursting, and they maintain their shape and function. Therefore, the correct answer is option C: They will swell but will not burst.