Question

Calculate the number of photons emitted per second by a $10\text{W}$ sodium vapour lamp. Assume that $60\%$ of the consumed energy is converted into light. Wavelength of sodium light is $662\text{nm}$.
(Given that $h=6.62\times {10}^{-34}\text{J s}$)

• A. $2\times {10}^{19}$
• B. $3\times {10}^{19}$
• C. $2\times {10}^{20}$
• D. $3\times {10}^{20}$

Answer 1

The correct option is A $2\times {10}^{19}$

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

Since power is given as $10\text{W}$,
so energy consumed in $1$ sec is $10\text{J}$

But, given that $60\%$ of the consumed energy is converted into light.
So energy used $=6\text{J}$
Again, energy $\left(E\right)=n\frac{hc}{\lambda }=\frac{n\times 6.62\times {10}^{-34}\times 3\times {10}^8}{662\times {10}^{-9}}$
(Where n = number of photons)

So $6=\frac{n\times 6.62\times {10}^{-34}\times 3\times {10}^8}{662\times {10}^{-9}}$
$\Rightarrow n=\frac{6\times 662\times {10}^{-9}}{6.62\times {10}^{-34}\times 3\times {10}^8}$
$\Rightarrow n=2\times {10}^{19}$