The sun itself is a huge nuclear mechanism. It releases every day an amount of energy equal to that of millions of atomic bombs.
A nuclear bomb will not leave the slightest trace on the sun and will not alter its activity.
Moreover, since the solar atmosphere has a temperature of thousands of degrees, the bomb and its mechanism will melt long before it reaches the sun.
All that will reach the sun is a tiny cloud of radioactive material, and that’s it.
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75% of the Sun’s mass is composed of hydrogen atoms. Under the immense gravity and heat in the center of the star, these particles merge, creating helium atoms and releasing an enormous amount of energy.
This reaction is similar to what happens when launching hydrogen bombs, thousands of times more powerful than the bomb dropped on Hiroshima.
This process provides all the heat and light released by the Sun and allows life on Earth.
A way to signal our existence to other intelligent beings
The atomic bomb itself would have no serious effect on the sun, but if we threw a bunch of plutonium into it, other advanced societies might notice.
Plutonium is an artificial element. And would not naturally occur in the sun, so anyone who noticed it must conclude that someone else put it there.