Question

A 20% efficient bulb emits light of wavelength 4000 Å. If the power of the bulb is 1 W, the number of photons emitted per second is ______.

[Take, h = 6.6 × 10^-34 J-s]

Options

• 4 × 10¹⁷

• 5 × 10¹⁵

• 4 × 10¹⁵

• 5 × 10¹⁷

Answer 1

A 20% efficient bulb emits light of wavelength 4000 Å. If the power of the bulb is 1 W, the number of photons emitted per second is 4 × 10^17.

Explanation:

Efficiency = `("Output power" ("P"_"o"))/("Input power" ("P"_"i"))`

⇒ `20% = ("P"_"o")/("P"_"i")`

⇒ `0.2 = ("P"_"o")/1`                    [P_i = 1]

⇒ P_o = 0.2 ...............(i)

The number of photons emitted per second is given as,

n = `"Output power"/"Energy of one photon" = "P"_"o"/(("hc")/lambda) = ("P"_"o"lambda)/("hc")`

= `(0.2 xx 4000 xx 10^-10)/(6.6 xx 10^-34 xx 3 xx 10^8) = 0.04 xx 10^19 = 4 xx 10^17`