Question

The number of photons emitted in 10 hours by a 60 w sodium lamp will be

Answer 1

Given , Power = 60W
time = 10 hours = 10 × 3600 sec = 3.6 × 10⁴ sec
We know, Energy = Power × time
so, Energy = 60W × 3.6 × 10⁴ sec = 21.6 × 10⁵J
Energy = 2.16 × 10⁶J

Now, A/C planks theory,
Energy of one photon = hc/λ ,
Here h is plank's constant and λ is wavelength of light emitted by sodium lamp.
you forgot to write wavelength of photon .
it is given λ = 5893 A° = 5.893 × 10⁻⁷ m
Now, Energy of one photon = 6.63 × 10⁻³⁴ × 3 × 10⁸/5.893 × 10⁻⁷
= 19.89/5.893 × 10⁻¹⁹ J

Now, number of photons = energy /energy of one photon
= 2.16 × 10⁶/{19.89/5.983 × 10⁻¹⁹}
= {2.16 × 5.893/19.89 }× 10²⁵
= 0.64 × 10²⁵
number of photons = 6.4 × 10²⁴

Answer 2

Here is the answer to your question:

Energy of photon, E = hν = h(c/λ) = 3.374 x 10-19 J

[It is known that, h = 6.626 x 10-34 m2 kg/s and c = 3 x 108 m/s]

Number of photons emitted by the sodium lamp in one second = [60 / 3.374 x 10-19]

∴ The number of photons emitted by the sodium lamp in 10 hours is

= [(60 x 10 x 3600)/ (3.374 x 10-19)] = 6.4 x 1024