If the H-atom electron in the n=1 state absorbs energy equivalent to 2.178x10^-18 J, what energy state will it occupy?
Doesn't that mean the electron is ionized?
Calculate the energy for an electron moving from n = infinity to n = 1.
dE = 2.178E-18(1/1 - 0)
dE = 2.178E-18
To answer this question, we need to understand the energy levels of the hydrogen atom. In the Bohr model, the energy levels of the hydrogen atom are given by the formula:
E = -13.6 eV / n^2
where E is the energy in electron volts (eV) and n is the principal quantum number.
To convert the given energy of 2.178x10^-18 J to eV, we can use the conversion factor:
1 eV = 1.602x10^-19 J
So, let's convert the given energy to eV:
2.178x10^-18 J * (1 eV / 1.602x10^-19 J) = 13.6 eV
Now, we can rearrange the formula above to solve for n. Rearranging the equation gives us:
n^2 = -13.6 eV / E
Plugging in the given E value of 13.6 eV:
n^2 = -13.6 eV / 13.6 eV = -1
Since the principal quantum number (n) cannot be negative, we conclude that there is no energy state for the hydrogen atom in this scenario.
Therefore, the H-atom electron will not occupy any energy state if it absorbs energy equivalent to 2.178x10^-18 J.