Explain why achievement of nuclear fusion in the laboratory requires a temperature of about 100 million degrees Celsius, which is much higher than that in the interior of the sun (15 million degrees Celsius).

The concept of the Coulomb Barrier is central to understanding nuclear fusion. Imagine the nuclei of atoms like magnets with the same charge; they naturally repel each other. In a nuclear fusion process, the nuclei must come so close that the nuclear force, which is much stronger than the Coulomb force but acts over smaller distances, can take over and bind them together, forming a heavier nucleus.

The thing is, overcoming the repulsive electrostatic force requires a lot of energy, which in the Sun, is provided by extreme pressure and temperature. In a laboratory, we aim to simulate these conditions, but we do not have the immense gravitational force like that in the Sun to create such high pressure. Therefore, we have to substantially increase the temperature to provide the nuclei enough kinetic energy to overcome the Coulomb Barrier. This is why temperatures of about 100 million degrees Celsius are necessary in a lab, in contrast to the 15 million degrees inside the Sun.

Kinetic energy in nuclear fusion plays a pivotal role as it's the energy of motion that the nuclei need to overcome the Coulomb Barrier. Here's a simple analogy: to get two opposing magnets to touch, you have to push them together with some force. In fusion, we don't physically push the nuclei; instead, we heat them up.

When particles are heated, they move faster. The hotter they get, the more kinetic energy they have, and the greater the chances that two nuclei will collide with enough force to overcome their repulsion. In the lab, we try to maximize this kinetic energy by cranking up the temperature. We use powerful lasers, magnetic fields, or electric currents in devices like tokamaks and inertial confinement fusion chambers to achieve these necessary conditions for nuclear fusion.

While both the Sun and a nuclear fusion laboratory aim to achieve nuclear fusion, the conditions under which they operate are vastly different. The Sun, a massive ball of gas, generates immense gravitational pressure at its core that naturally heats up and compresses the hydrogen atoms to the point where they can fuse.

In contrast, laboratories on Earth do not have that luxury. To achieve fusion, we need to create artificial environments where the temperature soars far beyond the natural conditions of the Sun's core. This is primarily because we cannot replicate the extreme pressure acting in the Sun's core, which significantly helps in overcoming the Coulomb barrier.

Understanding these differences highlights why achieving controlled nuclear fusion on Earth is a monumental challenge. It also explains why so much research and technological development is poured into finding reliable methods to initiate and sustain fusion reactions without requiring the behemoth energy input that would make the process impractical.