In which of the following groups of organisms are the cellular power plants, that is mitochondria, completely absent from their cells?

Introduction / Context:
Mitochondria are often called the power plants or power houses of the cell because they are the main sites of aerobic respiration and adenosine triphosphate (ATP) production in most eukaryotic cells. However, not all living cells possess mitochondria. This question tests whether you can correctly identify which of the listed groups completely lack mitochondria and therefore rely on different arrangements for energy production.

Given Data / Assumptions:

• Mitochondria are membrane bound organelles found in many cells.
• Options include bacteria and several groups of algae.
• We assume standard textbook level classification of prokaryotes and eukaryotes.

Concept / Approach:
The most important distinction here is between prokaryotic and eukaryotic cells. Prokaryotes, such as bacteria, do not have membrane bound organelles. They lack a true nucleus and also lack typical organelles like mitochondria, chloroplasts, and Golgi bodies. Their respiratory enzymes are located on the plasma membrane and infoldings of the membrane. In contrast, algae are eukaryotic organisms. Red algae, brown algae, and green algae all possess typical eukaryotic cell structures, including mitochondria, in addition to chloroplasts for photosynthesis.

Step-by-Step Solution:
Step 1: Separate the options into prokaryotes and eukaryotes. Bacteria are prokaryotic, while all types of algae listed are eukaryotic. Step 2: Recall that prokaryotes by definition lack membrane bound organelles such as mitochondria. Step 3: Understand that eukaryotic algae have mitochondria to carry out respiration in addition to chloroplasts for photosynthesis. Step 4: Conclude that among the given choices, only bacteria completely lack mitochondria.

Verification / Alternative check:
Standard cell biology diagrams show a bacterial cell without a nucleus or mitochondria, but with a nucleoid region and plasma membrane. Diagrams of algal cells, on the other hand, clearly include a nucleus and mitochondria. These visual comparisons confirm that mitochondria are characteristic of eukaryotes such as algae but not of prokaryotes like bacteria.

Why Other Options Are Wrong:

• Red algae: These are eukaryotic photosynthetic organisms that possess mitochondria along with chloroplasts containing red pigments.
• Brown algae: These multicellular algae also have mitochondria in their cells, which help support large body structures.
• Green algae: Green algae are considered closely related to land plants and clearly have typical plant like cell structures including mitochondria.

Common Pitfalls:
A common mistake is to assume that any photosynthetic organism does not need mitochondria because it has chloroplasts. In reality, even photosynthetic eukaryotes still carry out respiration in mitochondria. Another error is to forget the defining feature of prokaryotes, which is the absence of membrane bound organelles. Remember that this structural difference is the key to answering such questions quickly and accurately.

Final Answer:
Mitochondria are absent in bacteria, which are prokaryotic cells lacking membrane bound organelles.