Respuesta :
Answer:
The energy of a single photon is [tex]x= 37670.46eV[/tex]
The number of photon absorbed is [tex]z = 5.98*10^{8} \ photons[/tex]
Explanation:
From the question we are told that
The mass of tissue affected is [tex]m = 194g = \frac{194}{1000} = 0.194kg[/tex]
The energy realesed is [tex]E = 3.6 \mu J = 3.6 *10^{-6} J[/tex]
The wavelength is [tex]\lambda = 0.033nm = 0.033 *10^{-9}m[/tex]
Generally the energy of a sigle photon is mathematically rpresented as
[tex]E = \frac{hc}{\lambda }[/tex]
Where h is the Planck constant with a value of [tex]h =6.63*10^{-34} J \cdot s[/tex]
Substituting values
[tex]E = \frac{6.63*10^{-34}(3*10^8)}{0.033*10^{-9}}[/tex]
[tex]= 6.0272 *10^{-15}J[/tex]
Now
[tex]1 eV -------> 1.60*10^{-19}J[/tex]
[tex]xeV ---------> 6.02*10^{-15}J[/tex]
Making x the subject of the formula
[tex]x = \frac{6.02 *10^{-15}}{1.6 *10^{-19}}[/tex]
[tex]x= 37670.46eV[/tex]
The the number of photon absorbed is
[tex]z = \frac{The \ energy \ deliverd \ by \ to \ tissue }{The \ energy \ of \ a \ single \ photon}[/tex]
[tex]= \frac{3.6 *10^{-6}}{6.02*10^{-15}}[/tex]
[tex]z = 5.98*10^{8} \ photons[/tex]
The energy of the photon in eV is gotten as; E = 37599.3 eV
The number of photons absorbed during the dental x-ray is; n = 5.976 × 10^(8) photons
We are given;
Mass of the affected tissue; m = 194 g = 0.194 kg
Energy delivered by dental x-ray; E = 3.6 μJ = 3.6 × 10^(-6) J
Wavelength; λ = 0.033 nm = 0.033 × 10^(-9) m
Formula for energy of a photon is given as;
E = hc/λ
Where;
h is Planck's constant = 6.626 × 10^(-34) J.s
c is speed of light = 3 × 10^(8) m/s
Thus;
E = (6.626 × 10^(-34) × 3 × 10^(8))/(0.033 × 10^(-9))
E = 6.0236 × 10^(-15) J
Now, let's convert the energy to eV.
From conversion calculator online, we have;
E = 37599.31 eV
Now, to get the number of photons absorbed during the dental x-ray, we will use the formula;
n = (energy delivered by dental x-ray)/(energy delivered to a single photon)
Thus;
n = (3.6 × 10^(-6))/(6.0236 × 10^(-15))
n = 5.976 × 10^(8) photons
Read more about energy of photons at; https://brainly.com/question/17227537
