Cobalt-60 is a radioactive isotope used to treat cancers of the brain and other tissues. A gamma ray emitted by an atom of this isotope has an energy of 0.700 MeV (million electron volts; 1 eV = 1.602 * 10-19 J). What is the frequency (in Hz) and the wavelength (in m) of this gamma ray? Enter your answers in scientific notation.

1.69 x 10 ²⁰ Hz

1.77 x 10⁻¹² m

Explanation:

For any radiation, its energy is give by

E = hν = h c/λ where

h = Planck's constant,

ν = Frequency,

λ = wavelength,

c = speed of light

We have all the information so plug the values, being careful with the units.

E = h ν∴ ν = E/h

= (0.700 MeV x 1x10⁶ eV/MeV x 1.602 x 10⁻¹⁹ J/eV) / 6.626 x 10⁻³⁴ J s

= 1.69 x 10 ²⁰ s⁻¹ = 1.69 x 10 ²⁰ Hz (1 Hz = 1s⁻¹)

λ = c / ν = (3 x 10^8 m/s) / 1.69 x 10 ²⁰ s⁻¹ = 1.77 x 10⁻¹² m