Multiple Choice
Using the Bohr equation, calculate the wavelength (in nm) for the electron transition from n=4 to n=1 in the Lyman series.
9. Quantum Mechanics
Bohr Equation
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Calculate the wavelength of the light emitted when an electron in a hydrogen atom makes the transition from n=5 to n=2 using the Bohr equation.
A
656 nm
B
410 nm
C
486 nm
D
434 nm
Verified step by step guidance1
Identify the initial and final energy levels for the electron transition: n_initial = 5 and n_final = 2.
Use the Rydberg formula to calculate the wavelength of light emitted during the transition: \( \frac{1}{\lambda} = R_H \left( \frac{1}{n_{final}^2} - \frac{1}{n_{initial}^2} \right) \), where \( R_H \) is the Rydberg constant (1.097 x 10^7 m^-1).
Substitute the values for n_initial and n_final into the Rydberg formula: \( \frac{1}{\lambda} = 1.097 \times 10^7 \left( \frac{1}{2^2} - \frac{1}{5^2} \right) \).
Calculate the difference in the fractions: \( \frac{1}{4} - \frac{1}{25} \), and then multiply by the Rydberg constant.
Take the reciprocal of the result to find the wavelength \( \lambda \) in meters, and convert it to nanometers by multiplying by 10^9.
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