Answer:
THE INITIAL ENERGY LEVEL OF THE ELECTRON IS 1
Explanation:
Basically, the electron from the hydrogen atom moves from an unknown energy level to energy level 2, and the formula for calculating wavelength when the energy levels are given is;
y = wavelength = 410 nm = 410 *10^-9 m
Rh = Rydberg constant of hydrogen atom = 1.097 *10^7 m^-1
Z = atomic number of hydrogen = 1
n1 = initial energy level = ?
n2 = final energy level = 2
Substituting the values into the equation we get;
1 / 410 * 10^-9 = (1.097 *10^7) * (1^2) * ( 1 / n1^2 - 1 / 2^2)
1/ (410 *10^-9) (1.097 *10^7) = 1 /n1^2 - 1/ n2^2
1 / 4.4977 = 1/ n1^2 - 1/ 4
i/n1^2 = 1/4.4977 + 1/4
1 /n1^2 = 8.4977 / 17.9908
n1^2 = 17.9908 /8.4977;
n1^2 = 2.1171
n1 = square root of 2.1171
n1 = 1.455
n1 is approximately ≅ 1
So therefore the initial energy level of the electron in the hydrogen atom is 1