Question

A certain shade of blue has a frequency of 7.06 x 10" Hz. What is the energy of exactly one photon of this light? Planck's constant is h = 6.626 x 10 Js.

Answer 1

To calculate the energy of one photon of light, we can use the formula:

\[
E = h \cdot f
\]

where:
- \( E \) is the energy of the photon (in joules),
- \( h \) is Planck's constant (\(6.626 \times 10^{-34}\) J·s),
- \( f \) is the frequency of the light (in hertz).

Combining these values, we have:

Given:
- \( f = 7.06 \times 10^{14} \, \text{Hz} \)
- \( h = 6.626 \times 10^{-34} \, \text{Js} \)

Now we can calculate \( E \):

\[
E = (6.626 \times 10^{-34} \, \text{Js}) \cdot (7.06 \times 10^{14} \, \text{Hz})
\]

Calculating \( E \):

\[
E = 6.626 \times 7.06 \times 10^{-34} \times 10^{14}
\]

Calculating \( 6.626 \times 7.06 \):

\[
6.626 \times 7.06 = 46.88456
\]

So:

\[
E = 46.88456 \times 10^{-20} \, \text{J}
\]

Now converting this to significant figures (3 significant figures from the frequency), we have:

\[
E \approx 4.69 \times 10^{-19} \, \text{J}
\]

Thus, the energy of exactly one photon of this light is approximately:

\[
\boxed{4.69 \times 10^{-19} \, \text{J}}
\]