Question

Hospital x-ray generators emit x-rays with wavelength of about 15.0 nanometers (nm), where 1nm=10−9m. what is the energy of a photon of the x-rays?

Answer 1

A photon is characterized by either a wavelength, denoted by λ or equivalently an energy, denoted by E. There is an inverse relationship between the energy of a photon (E) and the wavelength of the light (λ) given by the equation: E=hc/λ E=hc/λ where h is Planck's constant and c is the speed of light. The value of these and other commonly used constants is given in the constants page. h = 6.626 × 10 -34 joule·s c = 2.998 × 108 m/s By multiplying to get a single expression, hc = 1.99 × 10-25 joules-m E=hc/λ (6.626*10^-34 J*s) x (2.998×10^8m/s)/ 1.5*10^-8 m = 1.32*10^-17 J

Answer 2

We have that  the energy of a photon of the x-rays is

$E=1.3*10^{-17}J$

From the Question we are told that

Wavelength $l=15.0 nm$

Generally the equation for energy of a photon is mathematically given as

$E=\frac{hc}{\lambda}$

Where

$h= 6.626*10^-{34}\\\\c=3.00*10^7m.s$

Therefore

$E=\frac{(6.626*10^-{34})(3.00*10^7)}{15*10^{-9}}$

$E=1.3*10^{-17}J$

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