What is the energy of light with a frequency of [tex]$3 \times 10^9 Hz$[/tex]?
[tex]\begin{array}{c}
h=6.626 \times 10^{-34} J \cdot s \\{[?] \times 10^{[?]} J}\end{array}[/tex]
Answer (2)
Use the formula E = h ν to calculate the energy of light.
Substitute the given values: E = ( 6.626 × 1 0 − 34 J ⋅ s ) × ( 3 × 1 0 9 Hz ) .
Calculate the energy: E = 1.9878 × 1 0 − 24 J .
The energy of light is 1.9878 × 1 0 − 24 J .
Explanation
Problem Analysis We are given the frequency of light as $3
\times 10^9 Hz an d Pl an c k ′ sco n s t an t a s h = 6.626
\times 10^{-34} J
\cdot s$. We need to find the energy of the light.
Energy Formula The energy of light is given by the formula $E = h
\nu , w h ere E i s t h ee n er g y , h i s Pl an c k ′ sco n s t an t , an d \nu$ is the frequency.
Substitution Substitute the given values into the formula: E = ( 6.626 × 1 0 − 34 J ⋅ s ) × ( 3 × 1 0 9 Hz ) .
Calculation Calculate the energy: E = 6.626 × 3 × 1 0 − 34 + 9 J = 19.878 × 1 0 − 25 J = 1.9878 × 1 0 − 24 J .
Final Answer Express the result in the required form: $1.9878
\times 10^{-24} J$.
Examples
Understanding the energy of light is crucial in various fields, such as telecommunications and medical imaging. For instance, when designing antennas for radio waves, engineers need to know the frequency and energy of the electromagnetic waves to optimize signal transmission and reception. Similarly, in medical imaging techniques like X-rays, the energy of the X-ray photons determines their penetration depth and the quality of the resulting images. By calculating the energy of light, we can better understand and utilize electromagnetic radiation in these applications.
The energy of light with a frequency of 3 × 1 0 9 Hz is calculated using the formula E = h ν . After substituting the given values, the energy is found to be 1.9878 × 1 0 − 24 J .
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