To use Planck's constant $h$ in a calculation where energy $E$ is given, you can apply the formula:

$E = h \cdot f$

Where:

• $E$ is the energy of the photon (in joules).
• $h$ is Planck's constant ($6.626 \times 10^{-34} \, \text{J} \cdot \text{s}$).
• $f$ is the frequency of the photon (in Hz).

Given: $E = 3.75 \times 10^{-16} \, \text{J}$

To find the frequency $f$, rearrange the formula:

$f = \frac{E}{h}$

Substitute the values:

$f = \frac{3.75 \times 10^{-16} \, \text{J}}{6.626 \times 10^{-34} \, \text{J} \cdot \text{s}}$

Now, let's calculate $f$:

$f \approx \frac{3.75 \times 10^{-16}}{6.626 \times 10^{-34}} \, \text{Hz}$

Let's compute that.The frequency $f$ corresponding to the energy $E = 3.75 \times 10^{-16}$ joules is approximately $5.66 \times 10^{17}$ Hz.

Would you like more details on this calculation or have any questions?

Here are some related questions to expand your understanding:

1. How is Planck's constant related to the energy of photons in different parts of the electromagnetic spectrum?
2. What are the implications of a photon having a higher frequency in terms of energy?
3. How does the energy of a photon relate to its wavelength?
4. Can you derive the wavelength of a photon from its frequency and Planck's constant?
5. How is Planck's constant used in quantum mechanics beyond just calculating photon energy?

Tip: Understanding the relationship between energy, frequency, and Planck's constant is key in quantum mechanics, especially in the study of light and other electromagnetic waves.