the mass of helium 4 atom is 6.64648 x 10^24 g and each of its two electrons has the mass 9.10939 x 10^-25 what fraction of the atoms mass is contributed by its nucleus?
To find the fraction of the helium-4 atom's mass contributed by its nucleus, we need to first calculate the total mass of the nucleus.
The helium-4 atom consists of two protons and two neutrons in its nucleus. We know that each proton and neutron has a mass of approximately 1.67 x 10^-24 grams. So, the total mass of the nucleus is:
Mass of nucleus = 2 protons * (1.67 x 10^-24 g/proton) + 2 neutrons * (1.67 x 10^-24 g/neutron)
= (2 * 1.67 x 10^-24 g) + (2 * 1.67 x 10^-24 g)
= 6.68 x 10^-24 g
Now, we can find the fraction of the helium-4 atom's mass contributed by its nucleus by dividing the mass of the nucleus by the total mass of the atom:
Fraction of mass contributed by nucleus = Mass of nucleus / Total mass of helium-4 atom
Total mass of helium-4 atom = Mass of nucleus + Mass of electrons
Given that the mass of the helium-4 atom is 6.64648 x 10^24 g and each electron has a mass of 9.10939 x 10^-25 g, we can substitute these values into the equation:
Total mass of helium-4 atom = 6.64648 x 10^24 g + 2 electrons * (9.10939 x 10^-25 g/electron)
= 6.64648 x 10^24 g + 2 * 9.10939 x 10^-25 g
= 6.64648 x 10^24 g + 1.821878 x 10^-24 g
= 6.828358 x 10^24 g
Now, we can calculate the fraction of the atom's mass contributed by its nucleus:
Fraction of mass contributed by nucleus = (6.68 x 10^-24 g) / (6.828358 x 10^24 g)
Note that we can simplify the fraction by cancelling out a factor of 10^24 from both the numerator and denominator:
Fraction of mass contributed by nucleus = (6.68) / (6.828358)
≈ 0.981 or 98.1%
Therefore, approximately 98.1% of the helium-4 atom's mass is contributed by its nucleus.