Question

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.

Answer 1

Energy of gamma rays is given by equation

$E = h\nu$

here we know that

h = Planck's constant

$\nu = frequency$

now energy is given as

$E = 4.70 MeV = 4.70 \times 10^6 \times 1.6 \times 10^{-19}$

$E = 7.52 \times 10^{-13} J$

now by above equation

$E = h\nu$

$7.52 \times 10^{-13} = 6.6 \times 10^{-34} \nu$

$\nu = 1.14 \times 10^{21} Hz$

now for wavelength we can say

$\lambda = \frac{c}{\nu}$

$\lambda = \frac{3\times 10^8}{1.14 \times 10^{21}}$

$\lambda = 2.63 \times 10^{-13} m$