Introduction:
B-trees and binary trees are two commonly used data structures in databases. Both have their advantages and disadvantages, but B-trees are preferred over binary trees in databases for several reasons.

Explanation:
1. Disk access is much slower than memory access:
- Disk access involves mechanical movements, such as the rotation of the disk and the movement of the read/write head, which takes significantly more time compared to accessing data from memory.
- B-trees are designed to minimize the number of disk accesses required to retrieve or update data. They achieve this by maximizing the number of keys stored in each node, reducing the height of the tree, and thus reducing the number of disk accesses needed.

2. Disk data transfer rates are much less than memory data transfer rates:
- Although disks have much higher capacities than memory, their data transfer rates are comparatively slower.
- B-trees are designed to optimize disk I/O by minimizing the amount of data that needs to be transferred between the disk and memory. By storing multiple keys in each node, B-trees reduce the overall amount of data that needs to be read from or written to the disk.

3. Disk capacities are greater than memory capacities:
- Disk capacities have increased significantly over the years and are now much larger than memory capacities.
- B-trees can efficiently utilize the larger disk capacities by storing a large number of keys in each node. This allows B-trees to store a larger amount of data on disk without sacrificing performance.

4. Disks are more reliable than memory:
- Disks are designed to be more reliable and durable compared to memory. They have mechanisms such as error correction codes and redundancy to ensure data integrity.
- B-trees take advantage of the reliability of disks by providing mechanisms like journaling and write-ahead logging, which guarantee the consistency of the database even in the event of system crashes or power failures.

Conclusion:
In conclusion, B-trees are preferred over binary trees in databases because disk access is much slower than memory access, disk data transfer rates are much less than memory data transfer rates, disk capacities are greater than memory capacities, and disks are more reliable than memory. B-trees optimize disk I/O and utilize larger disk capacities efficiently, providing better performance and data integrity in database systems.