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A difference of 5.4 eV separates two energy levels in an atom. What is the frequency of radiation emitted when the atom makes a transition from the upper level to the lower level? [1 eV=1.6×10⁻¹⁹ J, h=6.625×10⁻³⁴ J s]

Asked in GUJCET 2022 · Spectral series and wavelengths

• (1) 1.304×10¹⁵ Hz
• (2) 5.6×10¹⁵ Hz
• (3) 5.6×10¹⁴ Hz
• (4) 1.304×10¹⁴ Hz

Step-by-step solution

Why the other options are wrong

• (2) No single slip turns 5.4 eV into 5.6×10¹⁵ Hz. Sanity check: u=E/h=(8.64×10⁻¹⁹)/(6.625×10⁻³⁴)=1.304×10¹⁵ Hz.
• (3) 5.6×10¹⁴ Hz is the frequency for a gap of about 2.3 eV (h u=3.7×10⁻¹⁹ J), not 5.4 eV; no slip on the given numbers produces it.
• (4) 1.304×10¹⁴ Hz has the right digits but one power of ten too few: (10⁻¹⁹)/(10⁻³⁴)=10¹⁵.

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