In $1897,$ Wilhelm Wien derived a formula for blackbody radiation $($using thermodynamic arguments$)$ that for a time was believed to be correct. His formula, the Wien distribution law, is

$M_W(,T)d=\frac{2h{c}^2}{{}^5}$exp$(-h\frac{c}{}kT)d$

a$)$ Starting with eq $3\mathrm{.}1,$ find the expression for $M_w(v,T)dv($Hint: You will have to substitute both for $$ and for $d.)$

b$)$ Using your answer to part a$,$ find an expression for the total intensity of light predicted to be emitted by a blackbody according to Wien's distribution law.

$)$

$(u,T$

Does your result agree with the Stefan$-$Boltzmann expression $(($:$M(T)=T^4\}?$ If so$,$ find the value predicted for $($in units of $\frac{W}{m^2}*K^4,$ recalling that $W=$ watt $=\frac{J}{s}).($Note: In principle we could find $M_W(T)$ by integrating eq $3\mathrm{.}1,$ but in practice it is easier to do the integration over $v$ rather than over $.)$