Earth MAss if Helium and Hydrogen in suns propotions were added,

[TFM]

Homework Statement

The mass of silicon in the Earth is estimated to be 7x10^23 kg. The ratios of the masses of Hyrdogen and Helium to silicon in the sun are: H/Si = 850, He/Si = 250. Calculate the mass of the the body thatwould have been produced if H and He had been added to the Earth (present day mass M_E = 6x10^24 kg) in the smae proportions to Si as they are in the sun, esxpressing your answer as a multiple of M_E. How does this result compare with the mass of Saturn (= 100M_E)

Homework Equations

The Attempt at a Solution

does this question need me to convert the masses into number of molecules, or do I simply times the mass of Silicon by 250 and 850, and adde it to the mass of the the Earth?

Any help would be most appreciated,

TFM

 

[TFM]

If I just do it by mass an not atoms, I get a value of 5.95*10^26 for Hydrogen and 1.75*10^26 for Helium. Add this on to the mass of the Earth and I get 7.76*10^26, which is just over the mass of Saturn, does this look like the right thing to do?

TFM

 

[Moetasim]

I would approach this problem by first converting the mass of silicon in the Earth to the number of moles using its molar mass. Then, using the given ratios, I would calculate the number of moles of hydrogen and helium that would be present in the hypothetical body if they were added in the same proportions as in the sun. From there, I would convert the number of moles back to mass and add it to the mass of the Earth to get the total mass of the hypothetical body.

To answer the question of how this mass compares to that of Saturn, I would calculate the mass of Saturn using its given mass in terms of Earth's mass. Then, I would compare the two masses to see their relative sizes.

Overall, this hypothetical calculation would give us an idea of how much the Earth's mass would change if it had the same proportions of hydrogen and helium as the sun. However, it is important to note that this is a simplified calculation and does not take into account other factors such as the Earth's composition and the effects of gravity. Therefore, the result should be interpreted with caution.