Answer:
The value is [tex]N = 9.52 *10^{18} \ photons[/tex]
Explanation:
From the question we are told that
The power rating of the bulb is P = 25 W
The efficiency is [tex]\eta = 15\%[/tex]
The wavelength is [tex]\lambda = 505 \ nm = 505 *10^{-9} \ m[/tex]
Generally the energy of the photon emitted is mathematically represented as
[tex]E = \frac{h * c }{\lambda }[/tex]
Here h is the planks constant with a value [tex]h = 6.63*10^{-34} \ J \cdot s[/tex]
c is the speed of light with value [tex]c = 3.0*10^{8} \ m/s[/tex]
So
[tex]E = \frac{h * c }{\lambda }[/tex]
=> [tex]E = \frac{ 6.63*10^{-34} * 3.0 *10^{8} }{505 *10^{-9}}[/tex]
=> [tex]E = 3.9386 *10^{-19} \ J[/tex]
Generally we are told that 1 W = 1 J/s
Hence 25 W = 25 J
Generally the amount of this energy converted to light is
[tex]E_l = 25 * 0.15[/tex]
[tex]E_l = 25 * 0.15[/tex]
[tex]E_l = 3.75 \ J[/tex]
Generally the number of photons that are emitted by the light bulb per second is mathematically represented as
[tex]N = \frac{3.75}{ 3.9386 *10^{-19}}[/tex]
=> [tex]N = 9.52 *10^{18} \ photons[/tex]
