The Rydberg-Ritz equation describes the wavelengths of photons absorbed or emitted when electrons in the hydrogen atom undergo transitions between a lower energy level, nl and an upper energy level nu.If nl = 3 and nu= 6, what is the wavelength of a photon that is absorbed or emitted when an electron undergoes a transition between these states?Express answer in nanometres, rounded to the nearest whole number.
Question
The Rydberg-Ritz equation describes the wavelengths of photons absorbed or emitted when electrons in the hydrogen atom undergo transitions between a lower energy level, nl and an upper energy level nu.If nl = 3 and nu= 6, what is the wavelength of a photon that is absorbed or emitted when an electron undergoes a transition between these states?Express answer in nanometres, rounded to the nearest whole number.
Solution
The Rydberg-Ritz equation is given by:
1/λ = R * (1/nl² - 1/nu²)
where: λ is the wavelength of the emitted or absorbed photon, R is the Rydberg constant for hydrogen (approximately 1.097373 x 10^7 m^-1), nl is the principal quantum number of the lower energy level, nu is the principal quantum number of the upper energy level.
Given that nl = 3 and nu = 6, we can substitute these values into the equation to find λ:
1/λ = R * (1/3² - 1/6²) 1/λ = R * (1/9 - 1/36) 1/λ = R * (4/36) 1/λ = R * (1/9)
Therefore, λ = 1 / (R * 1/9)
Substituting the value of R, we get:
λ = 1 / (1.097373 x 10^7 m^-1 * 1/9) λ = 9 / (1.097373 x 10^7 m^-1) λ = 0.8206 x 10^-7 m
To convert this to nanometers (1 m = 10^9 nm), we multiply by 10^9:
λ = 0.8206 x 10^-7 m * 10^9 nm/m λ = 820.6 nm
Rounding to the nearest whole number, the wavelength of the photon that is absorbed or emitted when an electron in a hydrogen atom undergoes a transition from the energy level with nl = 3 to the energy level with nu = 6 is approximately 821 nm.
Similar Questions
The spectrum from a hydrogen vapour lamp is measured and four lines in the visible light range are observed. These lines are the so-called Balmer series, where an electron makes a transition from a higher level to the second energy level (nl=2).In this series, the transition from nu= 3 to nl= 2 produces the photon with the lowest energy, this corresponds to the line with the longest wavelength. This is measured to be λ = 646.9 nm.What value of the Rydberg constant R is obtained using these measurements?Express you answer in µm-1 to two decimal places
The energy E of the electron in a hydrogen atom can be calculated from the Bohr formula:=E−Ryn2In this equation Ry stands for the Rydberg energy, and n stands for the principal quantum number of the orbital that holds the electron. (You can find the value of the Rydberg energy using the Data button on the ALEKS toolbar.)Calculate the wavelength of the line in the emission line spectrum of hydrogen caused by the transition of the electron from an orbital with =n5 to an orbital with =n3. Round your answer to 3 significant digits.μm
An electron confined to an infinite potential well absorbs a photon with wavelength 𝜆. As a result, the electron makes a transition from the n = 1 state to the n = 7 state.What is the wavelength 𝜆' of the photon emitted when the electron makes a transition from the n = 4 state to the n = 1 state? (Give your answer as a decimal factor of 𝜆, eg write 2.5 if 𝜆' = 2.5 𝜆)
A hydrogen atom initially in the ground level absorbs a photon,which excites it to the n = 4 level. Determine the wavelength andfrequency of photon.
Which transition occurs when light with a wavelength of 434 nm is emitted by a hydrogen atom? Group of answer choicesThe electron falls from n=5 to n=2The electron falls from n=4 to n=2The electron jumps from n=2 to n=4The electron jumps from n=2 to n=5
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.