Final answer:
The false statement is that the Sun is 10 billion years old, which is incorrect; it is about 4.6 billion years old. Neutrinos, produced in the Sun's nuclear fusion process, carry energy away rapidly as they have a low interaction with matter. The correct option is b.
Step-by-step explanation:
The false statement about the Sun is that it is currently 10 billion years old. This assertion is not accurate because the Sun is estimated to be around 4.6 billion years old.
In contrast, the Sun is indeed producing neutrinos in its core, and the amount of helium in the Sun is increasing due to the process of nuclear fusion, where hydrogen nuclei fuse to form helium. This reaction happens at a core temperature of approximately 14 million kelvin.
A byproduct of multiple reactions in the core, neutrinos carry a minor portion of the energy produced in the Sun to its exterior, escaping rapidly due to their low interaction with matter. The neutrinos do not contribute to the transport of energy by conduction or convection; rather the energy they carry is lost to space almost immediately after being produced.
Hence, Option b is correct.