What is the radius in nm of the electron orbit of a hydrogen atom for n=3?
What is the radius in nm of the electron orbit of a hydrogen atom for n=4?
I mean I would like to know how to work it out and not just get the answer but thanks for the help.
The radius of the electron orbit in a hydrogen atom can be calculated using the Bohr radius formula. The formula is given by:
r = (0.529 × n²) / Z
Where:
- r is the radius of the electron orbit
- n is the principal quantum number
- Z is the atomic number of the nucleus, which is 1 for hydrogen
For n=3:
r = (0.529 × (3)²) / 1
r = (0.529 × 9) / 1
r = 4.761 nm
So, the radius of the electron orbit for n=3 is 4.761 nm.
For n=4:
r = (0.529 × (4)²) / 1
r = (0.529 × 16) / 1
r = 8.464 nm
So, the radius of the electron orbit for n=4 is 8.464 nm.
To calculate the radius of the electron orbit for a hydrogen atom with a given value of "n", we can use the formula derived from the Bohr model:
r = (0.529 * n^2) / Z
where:
- r represents the radius of the electron orbit in angstroms (Å)
- Z represents the atomic number (in this case, Z = 1 for hydrogen)
- n represents the principal quantum number, which determines the energy level or shell of the electron
To convert the radius from angstroms (Å) to nanometers (nm), we can use the conversion factor:
1 Å = 0.1 nm
Now, let's calculate the radius for n = 3:
r = (0.529 * 3^2) / 1 = 0.529 * 9 = 4.761 Å
1 Å = 0.1 nm, so 4.761 Å = 4.761 * 0.1 nm = 0.4761 nm
Therefore, the radius of the electron orbit for a hydrogen atom with n = 3 is approximately 0.4761 nm.
Next, let's calculate the radius for n = 4:
r = (0.529 * 4^2) / 1 = 0.529 * 16 = 8.464 Å
1 Å = 0.1 nm, so 8.464 Å = 8.464 * 0.1 nm = 0.8464 nm
Therefore, the radius of the electron orbit for a hydrogen atom with n = 4 is approximately 0.8464 nm.