A hydrogen atom’s electron moves from the n=4 level to the n=6 level. What is the wavelength of light associated with this transition? Is the light absorbed of emitted?
E = hc/λ
so, if you have the energy, just find λ.
1/wavelength = R*(n/4^2 - 1/6^2) where R is Rydberg's constant. You can find that on Google. You're going from 4 to 6 so you're absorbing energy.
To determine the wavelength of light associated with the transition of a hydrogen atom's electron from the n=4 level to the n=6 level, we can use the Rydberg formula:
1/λ = R_H * (1/n_f^2 - 1/n_i^2)
Where λ is the wavelength of the light, R_H is the Rydberg constant (approximately 1.097 x 10^7 m^-1), n_i is the initial energy level (n=4), and n_f is the final energy level (n=6).
Substituting the values into the formula:
1/λ = (1.097 x 10^7 m^-1) * (1/6^2 - 1/4^2)
1/λ = (1.097 x 10^7 m^-1) * (1/36 - 1/16)
1/λ = (1.097 x 10^7 m^-1) * (5/144 - 9/144)
1/λ = (1.097 x 10^7 m^-1) * (-4/144)
Simplifying:
1/λ = -0.0304 x 10^7 m^-1
λ = -1/(-0.0304 x 10^7 m^-1)
λ ≈ 32.89 x 10^-7 m
λ ≈ 328.9 nm
The positive wavelength value indicates that light is emitted during this transition.
To find the wavelength of light associated with the electron transition in a hydrogen atom, we can use the Rydberg formula. The Rydberg formula is given by:
1/λ = R * (1/n₁² - 1/n₂²)
Where:
- λ is the wavelength of light
- R is the Rydberg constant, approximately 1.097 x 10⁷ m⁻¹
- n₁ and n₂ are the principal quantum numbers of the initial and final states of the electron, respectively
In this case, the electron moves from the n=4 level to the n=6 level. Plugging the values into the formula, we have:
1/λ = (1.097 x 10⁷ m⁻¹) * (1/4² - 1/6²)
Simplifying the equation:
1/λ = (1.097 x 10⁷ m⁻¹) * (1/16 - 1/36)
1/λ = (1.097 x 10⁷ m⁻¹) * (9/144 - 4/144)
1/λ = (1.097 x 10⁷ m⁻¹) * (5/144)
1/λ = 5.68055556 x 10⁴ m⁻¹
Now, solving for λ:
λ = 1 / (5.68055556 x 10⁴ m⁻¹)
λ ≈ 1.758 x 10⁻⁵ m
Therefore, the wavelength of light associated with the electron transition from the n=4 level to the n=6 level is approximately 1.758 x 10⁻⁵ meters.
Now, to determine whether the light is absorbed or emitted, we need to consider the energy levels involved. When an electron moves from a higher energy level to a lower energy level, it releases energy in the form of light. This process is called emission. Conversely, if an electron absorbs energy and moves from a lower energy level to a higher energy level, it results in the absorption of light.
In this case, since the electron is transitioning from the n=4 level to the n=6 level (higher to lower), the light associated with this transition is emitted.