What is the wavelength of light emitted when an electron transitions from n=4 to

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Question: What is the wavelength of light emitted when an electron transitions from n=4 to n=2 in a hydrogen atom? (2020)

Options:

Correct Answer: 486 nm

Exam Year: 2020

Solution:

Using the Rydberg formula, the wavelength for the transition from n=4 to n=2 can be calculated to be approximately 486 nm.

What is the wavelength of light emitted when an electron transitions from n=4 to n=2 in a hydrogen atom? (2020)

What is the wavelength of light emitted when an electron transitions from n=4 to n=2 in a hydrogen atom? (2020)

Step 1: Understand that in a hydrogen atom, electrons can exist in different energy levels, which are represented by 'n' values. Here, n=4 is the higher energy level and n=2 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 (2), and n2 is the higher energy level (4).
Step 3: Plug in the values into the formula: 1/λ = 1.097 x 10^7 m^-1 * (1/2^2 - 1/4^2).
Step 4: Calculate the values inside the parentheses: 1/2^2 = 1/4 = 0.25 and 1/4^2 = 1/16 = 0.0625. So, 0.25 - 0.0625 = 0.1875.
Step 5: Now, substitute this back into the formula: 1/λ = 1.097 x 10^7 m^-1 * 0.1875.
Step 6: Calculate 1/λ = 2.060625 x 10^6 m^-1. To find λ, take the reciprocal: λ = 1 / (2.060625 x 10^6 m^-1).
Step 7: Calculate λ, which gives approximately 486 nm (nanometers).

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