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?
To determine the diameter of the atom in state number 50, we can use the relationship mentioned in the question that the diameter is proportional to n^2, where n is the energy level. In this case, we have n = 50.
Let's calculate the diameter using the formula:
diameter = (1x10^-10m) * n^2
Substituting the value of n = 50 into the formula, we have:
diameter = (1x10^-10m) * (50^2)
diameter = (1x10^-10m) * (2500)
diameter = 2.5x10^-7m
Therefore, the diameter of the atom in state number 50 is 2.5x10^-7m.
Now let's calculate how many unexcited atoms could fit within this one giant atom. To do this, we need to calculate the volume of the giant atom (sphere) and the volume of the unexcited atom (smaller sphere).
The volume of a sphere is given by the formula:
volume = (4/3) * π * (radius)^3
Since we have the diameter of the giant atom in state number 50, we can calculate its radius by dividing the diameter by 2:
radius_giant = (2.5x10^-7m) / 2
Using this radius value, we can calculate the volume of the giant atom.
Now, for the unexcited atom, we were not given its diameter or any other information about its size. Therefore, we cannot calculate its volume or compare it to the giant atom.
Hence, we are unable to determine how many unexcited atoms could fit within the giant atom based on the information provided.