To find the angular momentum of an electron in the hydrogen atom, we can use the formula:
L = n * h / (2 * π)
where L is the angular momentum, n is the principal quantum number, h is Planck's constant, and π is a mathematical constant approximately equal to 3.14159.
First, we need to determine the value of n for the electron in the 3.4 eV energy state. We can use the formula for the energy of an electron in a hydrogen atom:
E = -13.6 eV / n^2
where E is the energy of the electron and -13.6 eV is the energy of the electron in the ground state of the hydrogen atom.
Solving for n, we get:
n^2 = (-13.6 eV) / E
n^2 = (-13.6 eV) / (3.4 eV)
n^2 = 4
n = 2
Therefore, the electron is in the second energy level of the hydrogen atom.
Now, we can calculate the angular momentum using the formula above. Substituting the values, we get:
L = 2 * h / (2 * π)
L = h / π
We can approximate π as 3.14159 and use the value of Planck's constant as h = 6.626 x 10^-34 J s. Substituting these values, we get:
L = (6.626 x 10^-34 J s) / (3.14159)
L = 2.104 x 10^-34 J s
Therefore, the angular momentum of the electron in the second energy level of the hydrogen atom is 2.104 x 10^-34 J s.