Following results are observed when sodium metal is irradiated with different wavelengths. Calculate (a) Threshold wavelength and, (b) Planck’s constant.

λ (nm)	500	450	400
v × 10–5 (cm s–1)	2.55	4.35	5.35

<p>Let the threshold wavelength be λ₀ nm or λ₀ × 10⁻⁹ m.</p><p>h (ν−ν₀) = ½ mv²</p><p>hc (1/λ−1/λ₀)= ½ mv²</p><p>hc [ (1/500×10⁻⁹) – (1/ λ₀×10⁻⁹)] = ½ m (2.55×10⁶)² . (1)</p><p>Similarly, </p><p>hc [ (1/450×10⁻⁹) – (1/λ₀? ×10⁻⁹? )] = ½? m (4.35×10⁶)²&nbsp;. (2)</p><p>Similarly, </p><p>hc [ (1/400×10⁻⁹) – (1/λ₀? × 10⁻⁹? )] = ½? m (5.2 × 10⁶)²&nbsp;&nbsp;. (3)</p><p>Divide equation (2) by (1), </p><p> [ (λ₀ – 450) /450λ₀] x – [500λ₀/ (λ₀ – 500)] = (4.35/ 2.55)²</p><p> (λ₀ – 450)/ (λ₀ – 500) = 2.61</p><p>λ₀= 531 nm.</p><p>This is the threshold wavelength.</p><p>The value of the threshold wavelength is substituted in equation (3).</p><p>h ×3×10⁸ (1/400×10⁻⁹– 1/531×10⁻⁹)= ½ ×9.11×10⁻³¹× (5.2×10⁶)²</p><p>h=6.84×10⁻³⁴Js</p>

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