When uranium 92U235 decays, it emits a ray. If the emitted ray has a wavelength of 1.30 x 10-11 m, determine the energy (in MeV) of the ray
ε=hc/λ=
=6.63•10^-34•3•10^8/1.3•10^-11=
=1.53•10^-14 J =1.53•10^-14/1.6•10^-19=
=95625 eV=0.095625 MeV
When uranium 92U235 decays, it emits a ray. If the emitted ray has a wavelength of 1.16 × 10-11 m, determine the energy (in MeV) of the ray.
To determine the energy of the emitted ray, you can use the equation:
Energy (E) = Planck's constant (h) * Speed of light (c) / Wavelength (λ)
The energy unit we're using here is MeV (mega-electron volts), and the speed of light is approximately 3.00 x 10^8 m/s.
First, convert the wavelength from meters to nanometers (since the wavelength is given in scientific notation):
1.30 x 10^-11 m = 1.30 x 10^1 nm (because 1 nm = 10^-9 m)
Now we can substitute the values into the equation:
E = (Planck's constant) * (Speed of light) / (Wavelength)
E = (6.63 x 10^-34 J·s) * (3.00 x 10^8 m/s) / (1.30 x 10^1 nm)
We also need to convert the energy to MeV. 1 MeV is equal to 1.602 x 10^-13 Joules.
E (in MeV) = [(Planck's constant) * (Speed of light) / (Wavelength)] / (1.602 x 10^-13 J)
Substituting the given values:
E (in MeV) = [(6.63 x 10^-34 J·s) * (3.00 x 10^8 m/s) / (1.30 x 10^1 nm)] / (1.602 x 10^-13 J)
Now, calculate the result using a calculator:
E (in MeV) ≈ 7.55 MeV
Therefore, the energy of the emitted ray is approximately 7.55 MeV.