What is the wavelength of light emitted when an electron transitions from n=3 to

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Question: What is the wavelength of light emitted when an electron transitions from n=3 to n=1 in a hydrogen atom? (2020)

Options:

Correct Answer: 102.6 nm

Exam Year: 2020

Solution:

Using the Rydberg formula, the wavelength for the transition from n=3 to n=1 can be calculated to be approximately 102.6 nm.

What is the wavelength of light emitted when an electron transitions from n=3 to n=1 in a hydrogen atom? (2020)

What is the wavelength of light emitted when an electron transitions from n=3 to n=1 in a hydrogen atom? (2020)

Step 1: Understand that in a hydrogen atom, electrons can occupy different energy levels, which are represented by 'n' values. Here, n=3 is the higher energy level and n=1 is the lower energy level.
Step 2: Use the Rydberg formula to calculate the wavelength of light emitted during the transition. The formula is: 1/λ = R * (1/n1^2 - 1/n2^2), where R is the Rydberg constant (approximately 1.097 x 10^7 m^-1), n1 is the lower energy level (1), and n2 is the higher energy level (3).
Step 3: Plug in the values into the formula: 1/λ = 1.097 x 10^7 m^-1 * (1/1^2 - 1/3^2).
Step 4: Calculate the values inside the parentheses: 1/1^2 = 1 and 1/3^2 = 1/9, so 1 - 1/9 = 8/9.
Step 5: Now, substitute back into the formula: 1/λ = 1.097 x 10^7 m^-1 * (8/9).
Step 6: Calculate 1/λ = (1.097 x 10^7 * 8/9) m^-1, which gives you approximately 9.73 x 10^6 m^-1.
Step 7: Take the reciprocal to find λ: λ = 1 / (9.73 x 10^6 m^-1).
Step 8: Calculate λ, which gives you approximately 1.03 x 10^-7 m, or 102.6 nm.

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