Question

An excited atom gives up its excess energy by emitting a photon of certain characteristic frequency. The average time period that elapses between the excitation of an atom and the time it radiates is $1.0\times {10}^{-8}s$. What is the inherent uncertainty in the frequency of the photon?

• A. $8\times {10}^{6}Hz$
• B. $8\times {10}^{7}Hz$
• C. $8\times {10}^{8}Hz$
• D. $8\times {10}^{9}Hz$

Answer 1

The correct option is A $8\times {10}^{6}Hz$

The relation between uncertainty in energy and uncertainty in time is given by
$\Delta E.\Delta t\ge \frac{\hslash }{2}$

Here, $\Delta t=1\times {10}^{-8}s$

$\Rightarrow \Delta E\ge \frac{1.05\times {10}^{-34}}{2(1\times {10}^{-8})}$
i.e $\Delta E\ge 5.3\times {10}^{-27}J$

But energy of photon $E=h\nu \Rightarrow \Delta E=h\Delta \nu$
Therefore, uncertainty in frequency
$\Delta \nu =\frac{\Delta E}{h}$
i.e $\Delta \nu \ge 8\times {10}^{6}Hz$