suppose that the charge on the electron and proton did not have the same magnitude but instead differed by one part in 10^10. What would be the net charge on a 1.0 kg sample of helium gas?
1000 g of He is 250 moles
It would contain 250 Nav He atoms and 500 Nav protons and electrons.
(Nav is Avogadro's number)
Multiply 250 Nav by 10^-10 of the proton charge (e), and you get a net charge of
250*6.02*10^23*1.6*10^-29 C = 0.00241 C
the difference of charge between one electron and one proton will be equal to(1.6*10^-19)*(1/10^10), since there are two electrons and two protons in helium, multiply by 2 to get the charge of one atom of helium.
number of moles of He:
n(He)= m/M = 1000g/4g/mol = 250 mol
number of atoms of He:
N(He)= n*Na = 250*6.022*10^23.
so charge of 1kg of helium = 250*6.022*10^23*2*(1.6*10^-19)*(1/10^10) = 4.8*10^-3 C or 4.8 mc
To determine the net charge on a 1.0 kg sample of helium gas, we need to consider the number of electrons and protons in the sample.
Let's first establish the number of helium atoms in the sample. The atomic mass of helium (He) is approximately 4 atomic mass units (amu). Since 1 amu is defined as 1/12 the mass of a carbon-12 atom, we can calculate the number of moles of helium using the following equation:
moles of helium = mass of helium sample / molar mass of helium
Given that the mass of the helium sample is 1.0 kg (or 1000 grams) and the molar mass of helium is approximately 4 grams/mol, we have:
moles of helium = 1000 g / 4 g/mol = 250 mol
Since 1 mole of helium contains Avogadro's number (6.022 x 10^23) helium atoms, we can calculate the total number of helium atoms in the sample:
number of helium atoms = moles of helium × Avogadro's number
= 250 mol × (6.022 × 10^23 atoms/mol)
≈ 1.5055 × 10^26 atoms
Now let's consider the charge imbalance due to the difference in charge magnitude between electrons and protons. If the charge on the proton differs from the charge on the electron by one part in 10^10, we can calculate the fractional charge imbalance as:
fractional charge imbalance = 1 / (10^10)
Now, each helium atom consists of two protons and two electrons. Therefore, the net charge on each helium atom would be twice the fractional charge imbalance:
net charge on each helium atom = 2 × fractional charge imbalance
Finally, to determine the net charge on the 1.0 kg sample of helium gas, we multiply the net charge on each helium atom by the total number of helium atoms:
net charge on helium gas sample = net charge on each helium atom × number of helium atoms
Substituting the values, we can calculate the net charge on the helium gas sample.