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What is the frequency of an x-ray wave with an energy of [tex]$2.0 \times 10^{-17} J$[/tex]?

Given:
[tex]\[ h = 6.626 \times 10^{-34} \, J \cdot s \][/tex]

Frequency: [tex][?] \times 10^{[?]} \, Hz[/tex]

Sagot :

GinnyAnswer
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.
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