What is the frequency of the most intense radiation from an object with temperature $100 ^ { \circ } \mathrm { C }$ ? The constant in Wien's law is $0.0029 \mathrm {~m} \cdot \mathrm { K } . \left( c = 3.0 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } \right)$
A) $1.0 \times 10 ^ { 11 } \mathrm {~Hz}$
B) $3.9 \times 10 ^ { 13 } \mathrm {~Hz}$
C) $2.9 \times 10 ^ { - 5 } \mathrm {~Hz}$
D) $1.0 \times 10 ^ { 13 } \mathrm {~Hz}$

Question

Quizplus · Accepted Answer

To find the frequency of the most intense radiation, we first convert the temperature from Celsius to Kelvin: $100 ^ { \circ } \mathrm { C } = 373 \mathrm { K }$. Then, we use Wien's displacement law in the form that relates temperature to wavelength: $\lambda_{\text{max}} = \frac{b}{T}$, where $b = 0.0029 \, \mathrm{m \cdot K}$ is Wien's constant, and $T$ is the temperature in Kelvin. Substituting $T = 373 \, \mathrm{K}$, we get $\lambda_{\text{max}} = \frac{0.0029}{373}$. To find the frequency ($f$), we use the relation $f = \frac{c}{\lambda}$, where $c = 3.0 \times 10^8 \, \mathrm{m/s}$ is the speed of light. Substituting the values, we calculate the frequency corresponding to the peak wavelength. The correct calculation leads to a frequency in the range of $10^{13}$ Hz, making option B the correct choice.

What Is the Frequency of the Most Intense Radiation from an Object