Question

An electrical discharge in a neon-filled tube maintains a steady population of $1.0\times {10}^9$atoms in an excited state with $\tau =20ns$. How many photons are emitted per second from atoms in this state?

Short answer

The number of photons emitted per second is$5.0\times {10}^{16}{s}^{-1}$

Step-by-step solution

Rate of photon emission;

In other words, rate of photon emission is equal to the rate of decay.

$r_{photon}=r_{decay}$

Rate of decay is equal to the ratio of the excited atoms and the lifetime of the excited state,

$r_{decay}=\frac{N}{\tau }$

Here,$N$is the number of excited atoms and$\tau$is the lifetime of excited state.

The rate of photon emission:

So, the rate of photon emission or the number of photons emitted per second is,

$r_{photon}=\frac{N}{\tau }$

Substitute $1.0\times {10}^9$for $N$and $20ns$for .

$$\begin{gathered} r_{photon}=\frac{1.0\times {10}^9}{20ns\left({\displaystyle \frac{1.0s}{{10}^{9}ns}}\right)} \\ =\frac{1.0\times {10}^9}{20\times {10}^{-9}s} \\ =5.0\times {10}^{16}{s}^{-1} \end{gathered}$$

Therefore, the number of photons emitted per second is$5.0\times {10}^{16}{s}^{-1}$