To determine the frequency of an X-ray photon given its energy, we employ the relationship between energy (E), Planck's constant (h), and frequency (f). This relationship is expressed by the formula:
[tex]\[ E = h \cdot f \][/tex]
Here:
- [tex]\( E \)[/tex] is the energy of the photon.
- [tex]\( h \)[/tex] is Planck's constant.
- [tex]\( f \)[/tex] is the frequency we need to find.
We can rearrange this formula to solve for the frequency (f):
[tex]\[ f = \frac{E}{h} \][/tex]
Given:
- The energy of the photon ([tex]\( E \)[/tex]) is [tex]\( 8.0 \times 10^{-15} \)[/tex] joules.
- Planck's constant ([tex]\( h \)[/tex]) is [tex]\( 6.63 \times 10^{-34} \)[/tex] joule seconds.
Substitute the given values into the formula:
[tex]\[ f = \frac{8.0 \times 10^{-15}}{6.63 \times 10^{-34}} \][/tex]
Perform the division:
[tex]\[ f = 1.206636500754148 \times 10^{19} \text{ hertz} \][/tex]
Thus, the frequency of the X-ray is approximately [tex]\( 1.2 \times 10^{19} \)[/tex] hertz.
Therefore, the correct answer is:
B. [tex]\( 1.2 \times 10^{19} \)[/tex] hertz
