Question

• An isolated macroscopic system at temperature 300K absorbs a photon from the visible part of spectrum (say Wavelength=500nm) obtain a value for the relative increase ∆w/w in The number of accessible states of the system ?

Answer 1

As per the given question,

Temperature (T)=300K

Wavelength $(\lambda)=500nm$

We know that $S=K_b\ln W$

Now, taking the differentiation,

$ds=K_b\frac{1}{W}dW$

$\frac{\Delta W}{W}=\frac{ \Delta S}{K_b}$

But we know that,

$\Delta S = \frac{Q}{T}=\frac{hc}{\lambda T}$

$={\frac{6.6\times 10^{-34}\times 3\times 10^8}{ 300K\times 500\times 10^{-9}}}$

$=1.326\times 10^{-21} J/K$

Hence,

$\frac{\Delta W}{W}=\frac{ \Delta S}{K_b}$

$=\frac{ 1.325\times 10^{-21}J/K}{1.38\times 10^{-23} J / K}$

$=96$