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Multiple Choice
Calculate the wavelength of the radiation released when an electron moves from n = 4 to n = 2 in a hydrogen atom using the Bohr equation.
A
486 nm
B
410 nm
C
434 nm
D
656 nm
Verified step by step guidance
1
Start by understanding the Bohr model, which describes the electron transitions in a hydrogen atom. The energy difference between two levels is given by the formula: , where is the Rydberg constant (approximately 2.18 x 10^-18 J) and is the principal quantum number.
Calculate the energy difference between the two levels using the formula: , where is the initial and final energy levels (n=4 and n=2).
Substitute the values into the formula: . Calculate the energy difference.
Use the energy difference to find the wavelength of the radiation using the formula: , where is Planck's constant (6.626 x 10^-34 J·s), is the speed of light (3.00 x 10^8 m/s), and is the wavelength.
Rearrange the formula to solve for wavelength: . Substitute the calculated energy difference into the equation and solve for .