What is the energy of a purple lamp with a frequency of [tex]7.5 \times 10^{14} Hz[/tex]?
[tex]h=6.626 \times 10^{-34} J \cdot s[/tex]
[?] x 10^[?] J

We use the formula E = h ν to calculate the energy of the purple lamp.
Substitute the given values: E = (6.626 \times 10^{-34} \text{ J \cdot s}) \times (7.5 \times 10^{14} \text{ Hz}) .
Calculate the product: E = 4.9695 × 1 0 − 19 J.
The energy of the purple lamp is 4.9695 × 1 0 − 19 J ​ .

Explanation

Understanding the Problem We are given the frequency of a purple lamp and Planck's constant, and we need to find the energy of the lamp. We know that the energy of a photon (like the light from the lamp) is related to its frequency by the equation:

E = h ν
where:

E is the energy of the photon,
h is Planck's constant ( 6.626 × 1 0 − 34 J ⋅ s),
ν is the frequency of the light ( 7.5 × 1 0 14 Hz).


Substituting the Values Now, we can plug in the given values into the formula:

E = (6.626 \times 10^{-34} \text{ J \cdot s}) \times (7.5 \times 10^{14} \text{ Hz})

Calculating the Energy Multiplying these values, we get:

E = 4.9695 × 1 0 − 19 J

Final Answer The energy of the purple lamp is 4.9695 × 1 0 − 19 J. We need to express this in the form [ ?] × 1 0 [ ?] J. So, the answer is:

4.9695 × 1 0 − 19 J
Examples
Understanding the energy of light is crucial in many applications, such as designing solar panels. Solar panels convert light energy into electrical energy, and knowing the energy of different colors of light helps engineers optimize the panel's efficiency. For instance, if a solar panel is designed to absorb purple light, knowing the energy of purple light allows engineers to calculate how much electricity the panel can generate. This principle is also used in other technologies like lasers and optical sensors, where precise control of light energy is essential.

Answered by GinnyAnswer | 2025-07-06