The hydrogen atom consists of a proton with an electron in orbit about the proton. The laws of quantum mechanics determine that the radius of this orbit is 5.29x10^-11 meters. Therefore, calculate
a) The electric potential the electron experiences.
b) The next available orbit has a radius four(4) times that of the orbit described above
c) When an electron goes from the higher energy orbit to lower energy orbit, it releases the change in energy as photon. What is the wavelength of the emitted photon.
a) The electric potential the electron experiences.
b) The next available orbit has a radius four(4) times that of the orbit described above
c) When an electron goes from the higher energy orbit to lower energy orbit, it releases the change in energy as photon. What is the wavelength of the emitted photon.
You will have to type your question, if cutting and pasting does not work.
If they want you to calculate the "velocity" of the electron, set
m V^2/R = k e^2, and solve for V.
But be warned that electrons do not really travel in circular orbits around nuclei. Quantum mechanics does not allow such simple models. The lowest Bohr orbit has no angular momentym at all. The electron is most likely to be found at the nucleus
The hydrogen atom consists of a proton with an electron in orbit about the proton. The laws of quantum mechanics determine that the radius of this orbit is 5.29x10^-11 meters. Therefore, calculate
a)The electric potential the electron experiences.
b)The next available orbit has a radius four(4) times that of the orbit described above
c)When an electron goes from the higher energy orbit to lower energy orbit, it releases the change in energy as photon. What is the wavelength of the emitted photon.
a) The electric potential is -ke^2/R, where
k is the Coulomb constant
R is the closest orbit
b) When r = 4R, the electric potential becomes -ke^2/4R^2
The wavelength emitted when the electron changes orbit is given by
hc/(wavelength) = E1 - E2
Both the kinetic and electric potential energy of the electron must be considered when calculating total electron energy, E.
To calculate the answers to the given questions, we will use the following formulas and constants:
1. The electric potential experienced by the electron is given by the formula:
Electric Potential (V) = (k * e) / r
Where:
- k is the electrostatic constant (9 x 10^9 Nm^2/C^2)
- e is the charge of the electron (-1.6 x 10^-19 C)
- r is the radius of the orbit
2. The next available orbit radius (r') is four times the initial orbit radius (r):
r' = 4 * r
3. The wavelength of the emitted photon is calculated using the formula:
Wavelength (λ) = hc / ΔE
Where:
- h is Planck's constant (6.626 x 10^-34 Js)
- c is the speed of light (3 x 10^8 m/s)
- ΔE is the change in energy
Now let's calculate the answers to each question:
a) Electric potential experienced by the electron:
- Substitute the given values into the formula:
V = (9 x 10^9 Nm^2/C^2 * -1.6 x 10^-19 C) / (5.29 x 10^-11 m)
- Calculate the electric potential to find the answer.
b) Radius of the next available orbit:
- Multiply the initial radius by 4 to obtain the next orbit's radius:
r' = 4 * (5.29 x 10^-11 m)
- Calculate the radius to find the answer.
c) Wavelength of the emitted photon:
- Calculate the change in energy (ΔE) by taking the difference of energy levels between the higher and lower orbits.
- Use the formula λ = hc / ΔE to calculate the wavelength of the photon.
Remember to plug in the corresponding values and perform the necessary calculations for each step.