Radiation, with wavelength 6561 Aᵒ falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of 3 × 10 –4 T. If the radius of the largest circular path followed by the electrons is 10 mm, the work function of the metal is close to :

Solution

Physics sir · 4 steps

The largest circle belongs to the fastest electron, so its radius gives you the maximum kinetic energy.

1. Photon energy. 6561 Å = 656.1 nm. Using hc = 1240 eV nm, each photon carries E = 1240/656.1 ≈ 1.89 eV.
2. Radius gives momentum. In the field, evB = mv²/r, so p = mv = eBr. The largest radius comes from the fastest electrons, which have the maximum kinetic energy.

   Kₘₐₓ = p²/2m = (eBr)²/2m

3. Put in numbers. eBr = 1.6 × 10⁻¹⁹ × 3 × 10⁻⁴ × 10⁻² = 4.8 × 10⁻²⁵ kg m s⁻¹. Then Kₘₐₓ = (4.8 × 10⁻²⁵)²/(2 × 9.1 × 10⁻³¹) = 1.27 × 10⁻¹⁹ J ≈ 0.79 eV.
4. So. By Einstein's equation, φ = E - Kₘₐₓ = 1.89 - 0.79 ≈ 1.1 eV, which is option (c).

The idea to keep. A magnetic field turns a speed into a radius: p = eBr. The largest radius gives the maximum kinetic energy, and then φ = hc/λ - Kₘₐₓ.

Answer from the NTA final answer key. Solution by PrepWiser.