Hi there, I need a little help starting this one.
Calculate the energy in joules needed to remove one electron in the n=1 state from a hydrogen atom.
I feel like i should apply the
wavelength = Nhc/deltaE but I have no idea how to apply this to hydrogen.
I appreciate your time!
Energy required to move an electron from one energy level to another is
delta E = E2-E1 = 2.180 x 10^-18/hc x (1/N1^2 - 1/N2^2) where N1 < N2.
So plug in N = 1 for N1 and infinity for N2 (since you want to remove the electron completely). That will make the 1/N2^2 part zero. Can you take it from there.
Hello! It seems like you're on the right track. The equation you mentioned, wavelength = Nhc/deltaE, relates the energy change, deltaE, to the wavelength of light emitted or absorbed during a transition. In this case, we can use it to calculate the energy needed to remove an electron from a hydrogen atom.
To get started, we need to determine the energy level difference between the n=1 state (initial state) and the unbound state (final state), where the electron is completely removed from the atom. In other words, we are looking for the ionization energy.
The ionization energy is the difference in energy between these two states. In the case of hydrogen, the energy difference can be found by using the Rydberg formula:
1/wavelength = R_H(1 - 1/n_f^2) - R_H(1 - 1/n_i^2)
Here, R_H is the Rydberg constant for hydrogen, which is approximately 2.18 × 10^-18 J, and n_i and n_f represent the initial and final energy levels, respectively. Since we are going from the n=1 state to the unbound state (meaning the electron is completely removed), the final state is essentially "infinity" or n_f = ∞.
By plugging in the values into the formula, the equation becomes:
1/wavelength = 2.18 × 10^-18 J (1 - 1/∞^2) - 2.18 × 10^-18 J (1 - 1/1^2)
Now, as we take the limit of n_f approaching infinity, remember that 1/∞ equals zero. So the equation simplifies to:
1/wavelength = 2.18 × 10^-18 J - 2.18 × 10^-18 J (1 - 1)
Simplifying further, we get:
1/wavelength = 2.18 × 10^-18 J
Now, solve for wavelength:
wavelength = 1 / (2.18 × 10^-18 J)
By calculating this, the wavelength will come out to be approximately 4.57 x 10^16 meters.
Finally, to find the energy needed to remove an electron, we can use the energy-wavelength relationship:
Energy = hc / wavelength
Plugging in the values, where h is Planck's constant (6.63 × 10^-34 J s) and c is the speed of light (3.00 × 10^8 m/s), we get:
Energy = (6.63 × 10^-34 J s × 3.00 × 10^8 m/s) / (4.57 × 10^16 meters)
Solving this equation will give you the energy in joules needed to remove one electron in the n=1 state from a hydrogen atom.
I hope this helps! Let me know if you have any further questions.