Following results are observed when sodium metal is irradiated with different wavelengths. Calculate (a) threshold wavelength and (b) Plancks constant. λ(nm) 500 450 400 v × 10⁵ (cms⁻¹) 2.55 4.35 5.35

Let the threshold wavelength be λ₀ nm or λ₀ × 10⁻⁹m.
h(ν - ν₀) = 1/2mv²
hc(1/λ - 1/λ₀) = 1/2mv²
hc(1/500 × 10⁻⁹ - 1/λ₀ × 10⁻⁹) = 1/2m(2.55 × 10⁵)² .. (1)
Similarly,
hc(1/450 × 10⁻⁹ - 1/λ₀ × 10⁻⁹) = 1/2m(4.35 × 10⁵)² .. (2)
Similarly,
hc(1/400 × 10⁻⁹ - 1/λ₀ × 10⁻⁹) = 1/2m(5.2 × 10⁵)² .. (3)
Divide equation (2) by (1),
(1/450 - 1/λ₀)/(1/500 - 1/λ₀) = (4.35/2.55)²
(500λ₀ - 225000)/(450λ₀ - 225000) = 2.91
500λ₀ - 225000 = 1309.5λ₀ - 641250
809.5λ₀ = 416250
λ₀ = 514.3 nm
It is the threshold wavelength.The value of the threshold wavelength is substituted in equation (3).
h × 3 × 10⁸(1/400 × 10⁻⁹ - 1/514.3 × 10⁻⁹) = 1/2 × 9.11 × 10⁻³¹ × (5.2 × 10⁵)²
h = 6.626 × 10⁻³⁴ Js