Question

Calculate the wavelength of light emitted when a hydrogen atom undergoes a transition from n=234 to n=233. Be sure your answer has the correct number of significant digits. Part 2 of 2 In what region of the electromagnetic spectrum does this wavelength fall? infrared microwave gamma rays visible uitraviolet

Answer 1

The wavelength of light emitted when a hydrogen atom transitions from n=234 to n=233 is approximately 1.217 × 10⁻³² meters, and it falls in the gamma rays region of the electromagnetic spectrum.

Step-by-step explanation:

To calculate the wavelength of light emitted when a hydrogen atom transitions from n=234 to n=233, we can use the formula:

wavelength = 1 / (R * (1/2332 - 1/2342))

where R is the Rydberg constant, which is approximately 1.097 × 107 m⁻¹.

Plugging in the values and evaluating the expression, we get a wavelength of approximately 1.217 × 10⁻³² meters. This wavelength falls in the gamma rays region of the electromagnetic spectrum.

Answer 2

The wavelength of light emitted when the hydrogen atom undergoes the specified transition is approximately 49.972 nanometers. As for the region of the electromagnetic spectrum, this wavelength falls in the ultraviolet region.

To calculate the wavelength of light emitted when a hydrogen atom undergoes a transition from n = 234 to n = 233, you can use the Rydberg formula:

1/λ = R_H * (1/n1² - 1/n2²)

Where:

- λ is the wavelength of light.

- R_H is the Rydberg constant for hydrogen, approximately 1.097 x 10^7 m^(-1).

- n1 is the initial quantum energy level (234 in this case).

- n2 is the final quantum energy level (233 in this case).

Now, plug in the values:

1/λ = (1.097 x 10^7 m^(-1)) * (1/234² - 1/233²)

1/λ = (1.097 x 10^7 m^(-1)) * (1/(54756) - 1/(54049))

Now, calculate the difference in fractions:

1/λ = (1.097 x 10^7 m^(-1)) * (0.00001826)

1/λ ≈ 20,017.22 m^(-1)

Now, calculate the wavelength (λ):

λ = 1 / (20,017.22 m^(-1))

λ ≈ 4.9972 x 10^(-5) meters

To express this wavelength in a more convenient unit, Convert it to nanometers (nm):

λ ≈ (4.9972 x 10^(-5) meters) * (1 x 10^9 nm/meter)

λ ≈ 49.972 nm