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In the photoelectric effect, the threshold wavelength of sodium is 5000 A. Find its work function. (h = 6.6×10⁻³⁴ J s; c = 3×10⁸ m s⁻¹; 1 eV = 1.6×10⁻¹⁹ J)

Asked in GUJCET 2009 · Work function and the photoelectric equation

• (1) 2.5 eV
• (2) 5.0 eV
• (3) 7.5 eV
• (4) 10 eV

Step-by-step solution

Why the other options are wrong

• (2) No single slip gives 5.0 eV -- it is double the right value and would need a threshold of about 2500 A. Sanity check: (hc)/(λ₀) = (1.98×10⁻²⁵)/(5×10⁻⁷) = 3.96×10⁻¹⁹ J = 2.48 eV.
• (3) No single slip gives 7.5 eV -- three times the right value; the threshold would then be near 1650 A. W = (hc)/(λ₀) = 2.48 eV.
• (4) No single slip gives 10 eV -- four times too large, matching a threshold of about 1240 A in the far ultraviolet. Sodium responds to visible light, so its work function is only a couple of eV.

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