Multiple Choice
If one photon of light has 2.68 × 10⁻¹⁸ J of energy, it has a wavelength of _____________ nm. Use the formula E = hc/λ, where h = 6.626 × 10⁻³⁴ J·s and c = 3.00 × 10⁸ m/s.
9. Quantum Mechanics
Wavelength and Frequency
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What is the wavelength of light emitted (in nm) when the electron in a hydrogen atom moves from n=4 to n=2?
A
486 nm
B
410 nm
C
434 nm
D
656 nm
Verified step by step guidance1
Identify the initial and final energy levels of the electron transition: n_initial = 4 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: \( \frac{1}{\lambda} = 1.097 \times 10^7 \left( \frac{1}{2^2} - \frac{1}{4^2} \right) \).
Calculate the difference in the fractions: \( \frac{1}{2^2} = \frac{1}{4} \) and \( \frac{1}{4^2} = \frac{1}{16} \), then find \( \frac{1}{4} - \frac{1}{16} \).
Solve for \( \lambda \) by taking the reciprocal of the result from the Rydberg formula calculation and convert the wavelength from meters to nanometers by multiplying by 10^9.
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