Hospital X-ray generators emit X rays with wavelength of about 15.0 nanometers (nm), where 1 nm=10-9m. What is the energy of a photon in an X ray?
To find the energy of a photon in an X-ray with a wavelength of 15.0 nanometers, we can use the formula:
E = hc / λ
where:
E is the energy of the photon,
h is the Planck's constant (6.626 x 10^-34 J·s),
c is the speed of light in a vacuum (2.998 x 10^8 m/s),
and λ is the wavelength.
First, we need to convert the wavelength from nanometers to meters:
15.0 nm = 15.0 x 10^-9 m
Now we can calculate the energy of the photon:
E = (6.626 x 10^-34 J·s * 2.998 x 10^8 m/s) / (15.0 x 10^-9 m)
E = (19.835 x 10^-26 J·m) / (15.0 x 10^-9 m)
E = 1.3223 x 10^-17 J
Therefore, the energy of a photon in an X-ray with a wavelength of 15.0 nanometers is approximately 1.3223 x 10^-17 Joules (J).
To find the energy of a photon in an X-ray, you can use the equation:
Energy (E) = Planck's constant (h) × speed of light (c) / wavelength (λ)
First, let's convert the wavelength from nanometers (nm) to meters (m) since the other values are in SI units:
15.0 nm = 15.0 × 10^(-9) m
Now we can substitute the values into the equation:
E = (6.626 × 10^(-34) J·s) × (3.00 × 10^8 m/s) / (15.0 × 10^(-9) m)
Simplifying the equation, we get:
E = (6.626 × 3.00) × (10^(-34) × 10^8) / (15.0 × 10^(-9))
E = 19.878 × 10^(-26) / 15.0
E = 1.3252 × 10^(-26) J
Therefore, the energy of a photon in an X-ray with a wavelength of 15.0 nm is approximately 1.3252 × 10^(-26) Joules.
E= hc/wavelength
E in joules in one photon.