The wavelength of the light beam is 497 nm.
Given,
Stopping Potential, V₀ = 1.00 eV
Work function, ϕ = 2.50 eV
Speed of light, c = 3 x 10⁸ m/s
Charge of electron, e = 1.6 x 10⁻¹⁹ C
Planck's constant, h = 6.63 × 10⁻³⁴ Js = 4.14 × 10⁻¹⁵ eVs
The expression for Einstein's photoelectric equation is:
KEₘₐₓ = E - ϕ ----- (1)
Where,
KEₘₐₓ is the maximum kinetic energy
E is the energy of the absorbed photons: E = hf
ϕ is the work function of the surface: ϕ = hf₀
The potential difference required to back all ejected electrons is called the Stopping Potential (V₀).
Stopping Potential (V₀) = KEₘₐₓ/e -----(2)
Substituting (2) into (1)
eV₀ = E - ϕ
1.6 x 10⁻¹⁹ x 1 = E - 2.50
E = 1.6 x 10⁻¹⁹ + 2.50
E = 2.50 eV
We know that,
E = hf
E = hc/λ [∵ f = c/λ]
λ = hc/E
λ = (4.14 × 10⁻¹⁵ × 3 x 10⁸) / 2.50
λ = 1240 × 10⁻⁹ / 2.50
λ = 496.8 × 10⁻⁹ m
λ = 497 × 10⁻⁹ m (approximately)
λ = 497 nm
Hence,
The wavelength of the light beam is 497 nm.
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