Question

An atom in an excited state has a $1.0\%$% chance of emitting a photon in$0.10ns$ . What is the lifetime of the excited state?

Short answer

The lifetime of the excited state is$10ns$.

Step-by-step solution

Given Information

We are given that atom in an excited state has a$1.0\%$chance of emitting a photon in$0.10ns$. We need to find the lifetime of the excited state.

Simplify

We are given with $P=1.0\%=0.01,∆t=0.10ns$, where $P$is percentage chances of emitting photon and $∆t$is time for emitting. To find lifetime of excited state, we will use the formula, $\tau =\frac{1}{r}$, where$r$is rate decay and $\tau$is lifetime of excited state . Let this be equation$1$.

So we need to find rate decay$r$, we will use the formula , $r=\frac{P}{∆t}$$=\frac{0.01}{0.10ns}=0.10$

Now we will put it in equation $1$, lifetime of excited staterole="math" localid="1650310365610" $\tau =\frac{1}{r}=\frac{1}{0.10}=10ns$