Answer
temperature in $^{0}C$ =4830.037 $^{0}C$
approximately 4830. $^{0}C$
Work Step by Step
From Plank's hypothesis $E=hf$
( where $f$ is frequency of radiation and $h$ is Planks constant
$h=6.63\times10^{-34} J.s$ )
so $f=\frac{E}{h}$
given $E$=$3.5\times10^{-19}J $
$f=\frac{3.5\times10^{-19}J}{6.63\times10^{-34} J.s}$
$f=0.5279034\times10^{15}/s$
$f=5.279\times10^{14} Hz$
this frequency corresponds to minimum energy of oscillation, so it is minimum frequency of radiation. Since wavelength is inversely proportional to frequency the wavelength corresponding to above frequency will be maximum
wavelength corresponding to above frequency $\lambda_{max}=\frac{c}{f}$
speed of light $c=3\times10^{8} m/s$
so $\lambda_{max}=\frac{3\times10^{8} m/s}{5.279\times10^{14} Hz}$
$\lambda_{max}=0.568289\times10^{-6} m$
$\lambda_{max} T= 2.90\times10^{-3}m.K$
$T= \frac{ 2.90\times10^{-3}m.K}{\lambda_{max}}$
$T= \frac{ 2.90\times10^{-3}m.K}{ 0.568289\times10^{-6} m}$
$T=5.103037\times10^{3}K$
$T= 5103.037 K$
absolute kelvin temperature = temperature in $^{0}C$ + 273
so temperature in $^{0}C$ = absolute kelvin temperature -273
so temperature in $^{0}C$ =5103.037 - 273
so temperature in $^{0}C$ =4830.037 $^{0}C$
