A 200 W sodium street lamp emits yellow light of wavelength 0.6μm. Assuming it to be 25% efficient in converting electrical energy to light, the number of photons of yellow light it emits per second is .
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Given:
Power of lamp = 200 W
Efficiency = 25 % = 0.25
The wavelength of yellow light, λ = 0.6 μm = 0.6 × 10⁻⁶ m
To Find:
The number of photons of yellow light emitted per second by the lamp.
Calculation:
- The electrical energy converted into light = Power × Efficiency
⇒ Total energy emitted per second = 200 × 0.25 = 50 J
- The energy of 1 photon = hc/λ
⇒ E = (6.63 × 10⁻³⁴ × 3 × 10⁸) / 0.6 × 10⁻⁶
⇒ E = 19.89 × 10⁻²⁶ / 0.6 × 10⁻⁶
⇒ E = 33.15 × 10⁻²⁰ J
- No of photons = Total energy / Energy of 1 photon
⇒ n = 50 / 33.15 × 10⁻²⁰
⇒ n = 1.508 × 10²⁰
- So, the number of photons of yellow light emitted per second by the lamp is 1.508 × 10²⁰.
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