Between which two orbits of the Bohr hydrogen atom must an electron fall to produce light of wavelength 434.2nm?
5,2
5,2 is correct.
To determine between which two orbits the electron must fall to produce light of a specific wavelength in the Bohr hydrogen atom, we can use the formula known as the Rydberg formula.
The Rydberg formula is given by:
1/λ = R * (1/n₁² - 1/n₂²)
Where:
λ is the wavelength of light emitted (in meters)
R is the Rydberg constant (approximately 1.097 × 10^7 m⁻¹)
n₁ and n₂ are the principal quantum numbers of the two orbits involved.
In this case, we are given the wavelength as 434.2 nm, which we need to convert to meters. Since 1 nm = 1 × 10⁻⁹ m, the wavelength can be expressed as:
λ = 434.2 nm * (1 × 10⁻⁹ m / 1 nm) = 434.2 × 10⁻⁹ m = 4.342 × 10⁻⁷ m
Now, plugging this value into the Rydberg formula, we have:
1/(4.342 × 10⁻⁷ m) = (1.097 × 10^7 m⁻¹) * (1/n₁² - 1/n₂²)
Since we want to find the values of n₁ and n₂, we can rearrange the equation:
1/n₁² - 1/n₂² = (4.342 × 10⁻⁷ m) / (1.097 × 10^7 m⁻¹)
To determine the possible values of n₁ and n₂, we can use trial and error or solve the equation numerically, perhaps by using a graphing calculator or software.
It is important to note that the Bohr model is a simplified model of the atom and does not fully capture the complexities of the electron's behavior. Nonetheless, for the purposes of this question, we can use the Rydberg formula as an approximation.