A photon has a frequency of [tex]\(7.3 \times 10^{-17} \text{ Hz}\)[/tex]. Planck's constant is [tex]\(6.63 \times 10^{-34} \text{ J} \cdot \text{s}\)[/tex].

The energy of the photon, to the nearest tenths place, is [tex]\(\square \times 10^{-50} \text{ J}\)[/tex].



Answer :

To determine the energy of a photon given its frequency and Planck's constant, we use the formula for energy of a photon:

[tex]\[ E = h \cdot f \][/tex]

where:
- [tex]\( E \)[/tex] is the energy of the photon,
- [tex]\( h \)[/tex] is Planck's constant ([tex]\(6.63 \times 10^{-34} \)[/tex] Joule-seconds),
- [tex]\( f \)[/tex] is the frequency of the photon ([tex]\(7.3 \times 10^{-17}\)[/tex] Hertz).

First, we substitute the given values into the formula:

[tex]\[ E = (6.63 \times 10^{-34}) \cdot (7.3 \times 10^{-17}) \][/tex]

Perform the multiplication:

[tex]\[ E = 6.63 \times 7.3 \times 10^{-34} \times 10^{-17} \][/tex]
[tex]\[ E = 48.399 \times 10^{-51} \][/tex]

Next, we simplify the result to match the form [tex]\( a \times 10^b \)[/tex], aiming for [tex]\(10^{-50}\)[/tex]:

[tex]\[ E = 4.8399 \times 10^{-50} \][/tex]

To express this value to the nearest tenth place, we look at the first decimal place and round accordingly:

[tex]\[ 4.8399 \approx 4.8 \][/tex]

Therefore, the energy of the photon is:

[tex]\[ 4.8 \times 10^{-50} \][/tex] Joules.