Radiation corresponding to the hydrogen transition 3→2 falls on a metal and produces photoelectrons. These electrons enter a magnetic field of 3 × 10⁻⁴ T. If the circular-path radius of the fastest electron is 10 mm, find the work function of the metal.
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Question

Radiation corresponding to the hydrogen transition 3→2 falls on a metal and produces photoelectrons. These electrons enter a magnetic field of 3 × 10⁻⁴ T. If the circular-path radius of the fastest electron is 10 mm, find the work function of the metal.

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G1 Physics · Accepted Answer

Step 1: For H transition 3→2, photon energy is 13.6(1/2²−1/3²)=1.89 eV. Step 2: The fastest photoelectron in B has momentum p=eBr. Step 3: With B=3×10⁻⁴ T and r=10 mm, K=p²/(2mₑ)≈0.79 eV. Hence work function φ≈1.89−0.79≈1.1 eV. Correct answer: D.