Question

A dental X‑ray typically affects 175 g of tissue and delivers about 4.05 μJ of energy using X‑rays that have wavelengths of 0.0235 nm. What is the energy in electron volts of a single photon of these X‑rays?

Answer 1

The energy of a single photon of X‑rays is
`E_v = 52898.9 \ eV`

Step-by-step explanation:

From the question we are told that

The mass of the tissue is
`m = 175 \ g = 0.175 \ kg`

The amount of energy delivered is
`E_T = 4.05 \mu J = 4.05 *10^(-6) \ J`

The wavelength is
`\lambda = 0.0235 \ nm = 0.0235 *10^(-9) \ m`

Generally the energy of a single photon is mathematically represented as

`E = (hc)/(\lambda )`

Where h is the Planck's constant with values
`h = 6.63 *10^(-34)\ J\cdot s`

and c is the speed of light with values
`c = 3.0 *10^(8) \ m/s`

Substituting values

`E = (6.63 *10^(-34) * 3.0*10^(8))/(0.0235 *10^(-9) )`

`E = 8.463 *10^(-15) \ J`

Converting this to electron volt we have

`E_v = 8.464 *10^(-15) * [(1 )/(1.6*10^(-19)) ]`

`E_v = 52898.9 \ eV`