What is the wavelength of an X-ray photon with energy 9.0 keV (9000 eV)? (1 eV = 1.60 × 10−19 joule.)
Express your answer to two significant figures and include the appropriate units.
0.14nm
Ah, the wavelength of an X-ray photon, how enlightening! Well, let's do some calculating, shall we?
First, we need to convert the energy from electron volts (eV) to joules (J). Since 1 eV is equal to 1.60 × 10−19 joule, we can multiply the energy by this conversion factor. So, 9000 eV times (1.60 × 10−19 J/eV) equals 1.44 × 10−15 joules.
Now that we have the energy in joules, we can use the equation E = hc/λ to find the wavelength (λ), where E is the energy, h is Planck's constant (6.63 × 10−34 J·s), and c is the speed of light (3.00 × 10^8 m/s). Plugging in these values, we get:
1.44 × 10−15 J = (6.63 × 10−34 J·s)(3.00 × 10^8 m/s) / λ
Now, let's solve for λ by rearranging the equation:
λ = (6.63 × 10−34 J·s)(3.00 × 10^8 m/s) / 1.44 × 10−15 J
Do some number crunching, and we find that the wavelength comes out to be approximately 1.37 × 10^-11 meters. So, rounding to two significant figures, the wavelength of the X-ray photon is 1.4 × 10^-11 meters.
Hope that brightened your day a bit!
To find the wavelength of an X-ray photon with an energy of 9.0 keV, we can use the relationship between energy and wavelength for photons, which is given by the equation:
E = hc/λ
Where E is the energy of the photon, h is Planck's constant (6.626 × 10^-34 J⋅s), c is the speed of light (3.00 × 10^8 m/s), and λ is the wavelength of the photon.
First, let's convert the energy from keV to joules:
1 eV = 1.60 × 10^−19 joules
9.0 keV = 9.0 × (1.60 × 10^−19) J
Now, we can calculate the wavelength using the rearranged equation:
λ = hc/E
Substituting the values:
λ = (6.626 × 10^-34 J⋅s × 3.00 × 10^8 m/s) / (9.0 × (1.60 × 10^−19) J)
Simplifying the expression:
λ = (1.9888 × 10^-25 J⋅m) / (9.0 × 1.60 × 10^-19 J)
λ = 1.9888 × 10^-25 J⋅m / 1.44 × 10^-18 J
Now, we can perform the division:
λ ≈ 1.38 × 10^-7 m
To express our final answer with two significant figures and appropriate units, we write:
The wavelength of an X-ray photon with an energy of 9.0 keV is approximately 1.4 × 10^-7 m or 140 nm.
E = hν so
E = 9.0*10^3 ev * 1.60*10^-19 J/ev = 1.44*10^-15 J
ν = E/h
λ = c/ν = ch/E