The atomic bomb is named as such because the explosion comes from splitting an atom. How do they do that?? And how do they make sure that it happens at the precise moment? How does an atomic bomb work?
How did they have the technology to do this in WWII when they didn't even have color TV?
The atomic bomb was sophisticated technology for its time, but you have to remember that a team of scientists spent most of the entire war furiously trying to create this technology. If color television would have ended the war or added to national defense, they would have been creating that!
I would have to agree with the above post, the reason it came before other inventions was the push by the government to be the first to create an atomic bomb. As mentioned above it was considered the only way to end the war without greater loss of American lives. I also think Truman wanted to send a message to the rest of the world.
The atomic bomb works when a large enough quantity of radioactive material, either plutonium or the isotope of uranium, U-235 is placed together. When this is done and a few of the atoms are split by bombarding them with high power neutrons, the atoms that react initially release many more high-power neutrons which react with other atoms. The number of atoms reacting grows exponentially and within a very short duration of time the whole quantity of radioactive material undergoes fission and in this process a huge amount of energy is released.
I think the reason behind the atomic bomb being created before many other inventions that required less research was because this was given the highest priority at that time. It was something that was considered a necessity to keep the US safe from the Japanese.
I can't tell you everything about how an atomic bomb works, but I can talk about your last point.
A) It's not like they couldn't make color TVs back then. The problem was that they couldn't make them cheap enough to be worth it.
B) The technology of the bomb itself was not that difficult. What was hard was making all of the uranium and plutonium that was needed for the bomb. Once they had figured that out, all they had to do was engineer the bomb. As you can see in the link below, all that involved was using a conventional explosion to fire one piece of uranium into the other.
So, the workings of the first atomic bombs weren't all that complicated and they put huge amounts of money into it. That's why they could do that and "couldn't" make a color TV.