The diameter of the atom is proportional to n2, where n = 1 labels the lowest, or "ground" state, n = 2 is the second state, n = 3 is the third state, and so on. If the atom's diameter is 1 multiplied by 10-10 m in its lowest energy state, what is its diameter in state number 46?
To find the diameter of the atom in state number 46, we can use the given information that the diameter is proportional to n^2, where n represents the energy state.
First, let's determine the ratio of the diameters of the atom between two energy states, n and m. We can calculate this by taking the ratio of the diameters:
(Diameter_n) / (Diameter_m) = (n^2) / (m^2)
Now, let's find the ratio between state 46 and the lowest ground state (n=1):
(Diameter_46) / (Diameter_1) = (46^2) / (1^2)
Simplifying the equation:
(Diameter_46) / (1 * 10^(-10) m) = (46^2) / (1^2)
Now, we can solve for the diameter of the atom in state number 46:
Diameter_46 = (Diameter_1) * (46^2) / (1^2)
Substituting the given value for the diameter in the lowest energy state (Diameter_1 = 1 * 10^(-10) m):
Diameter_46 = (1 * 10^(-10) m) * (46^2) / (1^2)
Using this formula, we can calculate the diameter of the atom in state number 46.