To find the frequency of a wave carrying a specific amount of energy, you can use the equation that relates energy (E) to frequency (f):
\[
E = h \cdot f
\]
where:
- \( E \) is the energy in joules,
- \( h \) is Planck's constant (\( 6.626 \times 10^{-34} , \text{J}\cdot\text{s} \)),
- \( f \) is the frequency in hertz (Hz).
Rearranging the formula to solve for frequency, you get:
\[
f = \frac{E}{h}
\]
Now, substituting the given energy \( 2.78 \times 10^{-15} , \text{J} \) into the equation:
\[
f = \frac{2.78 \times 10^{-15} , \text{J}}{6.626 \times 10^{-34} , \text{J}\cdot\text{s}}
\]
Calculating this:
\[
f \approx \frac{2.78 \times 10^{-15}}{6.626 \times 10^{-34}}
\]
\[
f \approx 4.19 \times 10^{18} , \text{Hz}
\]
So, the frequency of the wave is approximately \( 4.19 \times 10^{18} , \text{Hz} \).