Why doesn't helium in the sun's core undergo fusion?

The Sun's core is not yet hot enough, or under enough pressure, for helium fusion. Which is probably just as well, since when helium fusion begins, the Sun will swell into a red giant which will incinerate the Earth.

Fusion reactions need a certain amount of energy to get started. The energy, as indicated by the temperature, is simply too low in the sun's core (at THIS time) to fire up a helium fusion reaction. Wait a few billion years, and the amount of helium will build up so that the core will contract (thus compressing it and raising its temperature) to the temperature that He fusion can start.

In the core of the sun, helium is formed by the nuclear fusion of hydrogen isotopes.

helium is created in the solar core by combining hydrogen atoms in nuclear fusion.

Nuclear Fusion from hydrogen in it core and helium

Hydrogen undergoes nuclear fusion in the core of the sun to form helium.

Around the core of helium that been formed from hydrogen fusion.

Helium is formed in the core of the sun by the nuclear fusion reaction of hydrogen

No, it is formed by fusion of hydrogen and helium molecules.

Helium is formed in the core of the star (like the sun) by the nuclear fusion of hydrogen isotopes.

Because of the Thermonuclear fusion that goes on inside the core. Hydrogen nuclei undergo this process to form helium nuclei, giving out massive amounts of heat and light.

The Sun's energy is generated by nuclear fusion, the fusion of hydrogen into helium in the core of the Sun.

All red giant stars will start helium fusion when their core is compressed.

We understand that hydrogen atoms are fused into helium in the sun's core.

Not "on" the Sun but "in" the Sun, the Sun's core is where the nuclear fusion of hydrogen to helium is taking place.

hydrogen undergoes nuclear fusion to form helium atoms

Hydrogen fusion continues in a shell surrounding the core. Eventually the core is compressed enough to start helium fusion.

there is nuclear fusion going on in the core. first the sun pull hydrogen together into helium and after hydrogen is used out, helium is fusioned into carbon molecules.

When a main sequence star, such as our sun, exhausts it's supply of Hydrogen, fusion of Hydrogen to Helium ceases in the core. This results in cooling of the core and therefore causes it to contract. As the core contracts, the layers surrounding the star gain kinetic energy until the fusion of Hydrogen is possible in the outer layers. As these layers undergo fusion, they increase in temperature dramatically. The outer layers expand due to heat, and the star becomes massive; the main sequence star has evolved into a red giant. Fusion of Hydrogen to Helium continues in the outer layers, whilst the fusion of heavier elements such as carbon occurs in the core.

The fusion of Hydrogen into Helium in the core of the Sun is the source of the energy.

Nuclear Fusion in a Giant Star involves Helium being fused into a hydrogen shell that surrounds the core, and Nuclear Fusion in a Main-Sequence star involves Hydrogen being fused into Helium to produce Energy inside of the core.

Helium fusion occurs in the core of the stars that are in that stage of life where they have exhausted their hydrogen fuel and begin to burn helium. Wikipedia has some additional information and a link is provided.

The sun generates its fuel from nuclear fusion in the core. Like other stars, the sun has a core in which hydrogen nuclei combine in nuclear fusion to produce helium.

The energy source for stars, which produces vast amounts of heat and light, is the fusion of atomic nuclei in the star's core. In our own Sun, hydrogen is fused into helium; in older and heavier stars heavier elements may also undergo nuclear fusion.

Yes. The temperature and pressure at the sun's core allow nuclear fusion (Hydrogen in to Helium) to take place nonstop - a continuous chain reaction.