Did America drop the nuclear bombs on Japan because of the Russians?

No, the US did not use nuclear weapons on Japan because of the Russians. The use of these weapons forced Japan to surrender and ended World War 2.

America and its allies (including Russia) were at war with Germany and Japan during World War 2. The US developed the atomic bomb during this period, and decided to use it in an attempt to avoid having to invade the Japanese homelands. A landing on Japan and fighting with conventional weapons would have cost many thousands of lives on both sides, and with a nuclear option available, President Wilson chose to use it.

The first weapon ("Little boy") was dropped on Hiroshima. When this demonstration failed to cause Japan to surrender, a second weapon ("Fat Man") was dropped on Nagasaki. After the second blast, Japan threw in the towel and the war ended. Russia is not connected to the use of nuclear weapons on Japan. As stated, Russia was an ally of the US during World War 2. The Russians were busy taking all they could get in Europe after the fall of Germany while the US was dealing with Japan.