The correct answer is b) Thermonuclear.

Explanation:
During the 1950s, both the United States and the Soviet Union were engaged in the development and production of various types of weapons. However, the most significant and notable advancement in weapons technology during this period was the development of thermonuclear weapons.

1. Thermonuclear Weapons:
- Thermonuclear weapons, commonly known as hydrogen bombs, are a type of nuclear weapon that utilizes the process of nuclear fusion to release a tremendous amount of energy.
- These weapons are several orders of magnitude more powerful than fission weapons, which were developed earlier.
- The development of thermonuclear weapons marked a significant advancement in the destructive capabilities of nuclear weapons.

2. Fission Weapons:
- Fission weapons, such as atomic bombs, were developed during World War II and continued to be produced in the 1950s.
- These weapons work by splitting the nuclei of heavy atoms, such as uranium or plutonium, releasing a large amount of energy.
- Fission weapons were the first type of nuclear weapons to be used in warfare when the United States dropped atomic bombs on the Japanese cities of Hiroshima and Nagasaki in 1945.

3. Other Weapons:
- While thermonuclear and fission weapons were the primary focus of the US and USSR during the 1950s, both countries also developed and produced other types of conventional weapons.
- These weapons included various types of artillery, tanks, aircraft, and naval vessels, which were used to strengthen their respective military capabilities.

Conclusion:
During the 1950s, the United States and the Soviet Union primarily focused on the development and production of thermonuclear weapons. These weapons represented a significant advancement in destructive capabilities compared to fission weapons. Additionally, both countries continued to produce other conventional weapons to bolster their military strength.