Between which two orbits of the Bohr hydrogen atom must an electron fall to produce light of wavelength 434.2 ?
434.2 WHAT?
1/wavelength = R(1/ni^2 - 1/nf^2)
wavelength goes in in units of meters.
Look up the Rydberg constant
nf^2 = unknown
ni^2 = 2^2 = 4
Solve for the unknown.
To determine between which two orbits an electron must fall to produce light of a specific wavelength in the Bohr hydrogen atom, we can use the equation for the wavelength of light emitted during an electron transition:
1/λ = R(Z^2[(1/n1^2) - (1/n2^2)])
Where:
- 1/λ is the reciprocal of the wavelength of light emitted
- R is the Rydberg constant (approximately 1.097 × 10^7 m^-1)
- Z is the atomic number of the nucleus (for hydrogen, Z = 1)
- n1 and n2 are the initial and final principal quantum numbers, respectively
In this case, we are given the wavelength (λ) as 434.2 nm (converted to meters, λ = 434.2 × 10^-9 m).
Substituting these values into the equation, we can solve for the initial and final principal quantum numbers (n1 and n2). However, we need to determine the possible values of n1 and n2 that correspond to the given wavelength.
Let's use trial and error to find the appropriate values of n1 and n2.
We can start by assuming n1 = 1 and finding the corresponding n2 using the equation.
1/λ = R(Z^2[(1/n1^2) - (1/n2^2)])
1/434.2 × 10^-9 = 1.097 × 10^7 (1^2)[(1/n1^2) - (1/n2^2)]
Solving this equation will give us the value of n2 corresponding to n1 = 1. However, it is important to note that the electron can only transition to an orbit with a larger principal quantum number (n2 > n1).
If n2 obtained from the above equation is not an integer value, we can increment n1 by 1 and calculate the corresponding n2. We repeat this process until we find integer values of n1 and n2 that satisfy the given wavelength.
Once we determine the appropriate values of n1 and n2, the electron falls from the higher energy level (orbit with n2) to the lower energy level (orbit with n1) and emits light with a wavelength of 434.2 nm.