Chemistry · Bohr model of a hydrogen atom: its postulates, derivation of the relations for the energy of the electron and radii of the different orbits, limitations of Bohr's model
What is the wavelength of light emitted when the electron in hydrogen atom under
What is the wavelength of light emitted when the electron in hydrogen atom undergoes transition from the energy level with \( n=4 \) to energy level \( n=2 ? \) \( \left(\operatorname{given} R_{n}=109678 c m^{-1}\right) \)
- A. 786 nm
- B. 486 nm
- C. \( 586 \mathrm{nm} \)
- D. 986 nm
Step-by-step solution
Use Rydberg formula: 1/λ = R_H (1/n1^2 - 1/n2^2) with n1=2, n2=4. 1/λ = 109678 cm^{-1} (1/4 - 1/16) = 109678 × 3/16 = 20564.625 cm^{-1}. Then λ = 1/20564.625 cm = 4.8627×10^{-5} cm = 486.27 nm ≈ 486 nm.
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