Which of these particles would be able to pass freely through a cell membrane a) complex carbohydrate b) sodium ion c) protein d) oxygen molecule

The correct answer is d) oxygen molecule.

Cell membrane or a phosphate bilipid layer is semi-permeable in nature i.e. it allows selective molecules to pass through it.

Small and uncharged molecules can easily pass though it however, it prevents the movement of large and charged molecules.

Small and unchrged molecules usually move across the cell membrane by the method of simple diffusion. For example, gases like oxygen, carbon dioxide can easily move across the cell membrane depending upon their partial pressure.  Water moves by the process of osmosis across the cell membrane.

In contrast, charged or larger molecules such as ions, proteins, etc are transported across the cell membrane with the help of carrier proteins or channels in the plasma membrane.

For example, Na⁺/K⁺ pump help in transportation of sodium and potassium across the cell membrane, GLUT transporters are the members of membrane proteins which are associated with the transport of glucose across the cell etc.

during the process of dna replication, brdu can replace thymidine and incorporate into the newly synthesized dna, cell proliferation thus can be reflected in the extent of brdu incorporation.