Cobaltâ’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 4.70 MeV (million electron volts; 1 eV = 1.602 Ă— 10â’19 J). What is the frequency (in Hz) and the wavelength (in m) of this gamma ray? Enter your answers in scientific notation.

Respuesta :

Energy of gamma rays is given by equation

[tex]E = h\nu[/tex]

here we know that

h = Planck's constant

[tex]\nu = frequency[/tex]

now energy is given as

[tex]E = 4.70 MeV = 4.70 \times 10^6 \times 1.6 \times 10^{-19}[/tex]

[tex]E = 7.52 \times 10^{-13} J[/tex]

now by above equation

[tex]E = h\nu[/tex]

[tex]7.52 \times 10^{-13} = 6.6 \times 10^{-34} \nu[/tex]

[tex]\nu = 1.14 \times 10^{21} Hz[/tex]

now for wavelength we can say

[tex]\lambda = \frac{c}{\nu}[/tex]

[tex]\lambda = \frac{3\times 10^8}{1.14 \times 10^{21}}[/tex]

[tex]\lambda = 2.63 \times 10^{-13} m[/tex]