Can someone help me with this, i have started it but cant get it to work out.

The higher the energy level occupied by an electron in the hydrogen atom, the larger the atom. The diameter of the atom is proportional to n2, where n=1 labels the lowest, or “ground” state, n=3 is the third state, and so on. If the atom’s diameter is 1x10-10m in its lowest energy state, what is its diameter in state number 50? How many unexcited atoms could be fit within this one giant atom

what goes where?

d=1E-10*50^2

numberunexcited???=volumeexcited/volumeunexcited.

V=4/3 PI radius^3

The diameter increases by a factor of 50^2, so the volume increases by a factor of 50^6 = 1.56*10^10, compared to that of an atom in the n=1 state. That is approximately the number of n=1 atoms that can be fit inside the n=50 atom's volume, but the exact number depends upon how you "pack" them in. It will be closer to 1*10^10

To solve this problem, we first need to find the diameter of the atom in state number 50. We are given that the diameter of the atom in its lowest energy state is 1x10^-10 m, and we are told that the diameter is proportional to n^2, where n represents the energy level.

So, for state number 50, we can calculate the diameter using the given formula:
d = 1x10^-10 * 50^2

Now, simplify the expression:
d = 1x10^-10 * 2500
d = 2.5x10^-7 m

Therefore, the diameter of the atom in state number 50 is 2.5x10^-7 meters.

To find the number of unexcited atoms that could fit within this one giant atom, we need to compare the volumes of the excited and unexcited atoms.

The volume of a sphere is given by the formula:
V = (4/3) * π * radius^3

Since we are concerned with diameters, we must convert the diameter of the giant atom into a radius by dividing it by 2:
radius_giant_atom = 2.5x10^-7 / 2 = 1.25x10^-7 m

Now, we can calculate the volume of the giant atom:
V_giant_atom = (4/3) * π * (1.25x10^-7)^3

Next, we need to calculate the volume of an unexcited atom. We are not given a specific diameter for unexcited atoms, so let's assume they have the same diameter as the lowest energy state atom, which is 1x10^-10 m.

Therefore, the radius of an unexcited atom would be:
radius_unexcited_atom = 1x10^-10 / 2 = 5x10^-11 m

Now, we can calculate the volume of an unexcited atom:
V_unexcited_atom = (4/3) * π * (5x10^-11)^3

Finally, we can find the number of unexcited atoms that could fit within the giant atom:
number_unexcited_atoms = V_giant_atom / V_unexcited_atom

Simply substitute the calculated values into the formula to find the answer.