Calculate the number of photons emitted by a 100-W yellow lamp in 1.0 second. The wavelength of yellow light is 500 nm and assume hundred percent efficiency.

Question

Calculate the number of photons emitted by a 100-W yellow lamp in $1 \cdot 0$ second. The wavelength of yellow light is $500 nm$ and assume hundred percent efficiency.

Answer 1

Energy emitted by $100 W$ lamp $=$ power $\times$ time $=100 J s ^{-1} \times 1 \cdot 0 s =100 J$

Energy of a photon $=h v$

$=\frac{h c}{\lambda}=\frac{6.626 \times 10^{-34} J_{s} \times 3 \times 10^{8} ms ^{-1}}{500 \times 10^{-9} m } J =3.9756 \times 10^{-19} J$

Number of photons emitted $=\frac{100}{3 \cdot 9756 \times 10^{-19}}=2 \cdot 5 \times 10^{20} .$