To determine the frequency of an x-ray wave given its energy and Planck's constant, we can use the relationship given by Planck's equation:
[tex]\[ E = h \cdot f \][/tex]
where:
- [tex]\( E \)[/tex] is the energy of the wave,
- [tex]\( h \)[/tex] is Planck's constant, and
- [tex]\( f \)[/tex] is the frequency of the wave.
We need to solve for [tex]\( f \)[/tex], the frequency. Rearranging the formula to solve for [tex]\( f \)[/tex]:
[tex]\[ f = \frac{E}{h} \][/tex]
Given:
- [tex]\( E = 2.0 \times 10^{-17} \)[/tex] Joules,
- [tex]\( h = 6.626 \times 10^{-34} \)[/tex] Joule-seconds,
Substituting the given values into the formula:
[tex]\[ f = \frac{2.0 \times 10^{-17}}{6.626 \times 10^{-34}} \][/tex]
Carrying out the division:
[tex]\[ f = 3.018412315122246 \times 10^{16} \text{ Hz} \][/tex]
Thus, the frequency of the x-ray wave is:
[tex]\[ 3.018412315122246 \times 10^{16} \text{ Hz} \][/tex]
This is the detailed step-by-step calculation to determine the frequency of the x-ray wave given its energy and Planck's constant.
