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?

diameter=1E-10*50^2 according to the problem statement.

numberunexcited=volumeexcited/volumeunexcited.

V=4/3 PI radius^3

To determine the diameter of the atom in state number 50, we'll use the given information that the diameter of the atom in its lowest energy state (n=1) is 1x10^-10 m and that the diameter is proportional to n^2.

The diameter of the atom in state number 50 can be calculated using the formula:

Diameter = Diameter(n=1) * (n^2)

Let's substitute the values in:

Diameter(50) = (1x10^-10) * (50^2)

Calculating the right-hand side of the equation:

Diameter(50) = (1x10^-10) * (2500)

Diameter(50) = 2.5x10^-7

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

Now, let's determine how many unexcited atoms could fit within this giant atom. To do this, we need to find the volume of the giant atom and the volume of an unexcited atom.

The volume of a sphere is given by the formula:

Volume = (4/3) * pi * (radius)^3

Since we have the diameter, we can calculate the radius by dividing the diameter by 2:

Radius = Diameter(50) / 2 = (2.5x10^-7) / 2 = 1.25x10^-7

Now, let's calculate the volume of the giant atom:

Volume(giant atom) = (4/3) * pi * (radius)^3
Volume(giant atom) = (4/3) * pi * (1.25x10^-7)^3

Next, we need to find the volume of an unexcited atom, which has a diameter of 1x10^-10 meters:

Volume(unexcited atom) = (4/3) * pi * ((1x10^-10)/2)^3

Finally, we can determine how many unexcited atoms could fit within the giant atom by dividing the volume of the giant atom by the volume of an unexcited atom:

Number of unexcited atoms = Volume(giant atom) / Volume(unexcited atom)

Calculate the right-hand side of the equation using the previously calculated volumes and the formula:

Number of unexcited atoms = (Volume(giant atom)) / (Volume(unexcited atom))

Please calculate the volumes and substitute the values to find the final answer.