Question

Calculate the number of photons emitted per second by a 10 W sodium vapour lamp. Assume that 50% of the consumed energy is converted into light. Wavelength of sodium light = 600 nm. Take $h=6.6\times {10}^{-34}Jsandc=3\times {10}^{8}m{s}^{-1}$

• A. $15.15\times {10}^{18}$
• B. $25.25\times {10}^{18}$
• C. $2.52\times {10}^{19}$
• D. $1.51\times {10}^{18}$

Answer 1

The correct option is A $15.15\times {10}^{18}$

We know, power is the energy transferred or converted per unit time.

Since power is given as 10 W,
so energy consumed in 1 sec is = 10 J

But, given that 50 % of the consumed energy is converted into light.
So energy used = 5 J
Again, energy $\left(E\right)=n\frac{hc}{\lambda }=\frac{n\times 6.6\times {10}^{-34}\times 3\times {10}^8}{600\times {10}^{-9}}$
(Where n = number of photons)

So $5=\frac{n\times 6.6\times {10}^{-34}\times 3\times {10}^8}{600\times {10}^{-9}}$
$\Rightarrow n=\frac{5\times 600\times {10}^{-9}}{6.6\times {10}^{-34}\times 3\times {10}^8}$
$\Rightarrow n=15.15\times {10}^{18}$