Question

The gamma rays emitted by ${}^{\mathbf{60}}\mathbf{Co}$are used in radiation treatment of cancer. They have a frequency of $\mathbf{2}\mathbf{.}\mathbf{83}\mathbf{\times }{\mathbf{10}}^{\mathbf{20}}{\mathbf{s}}^{\mathbf{-}\mathbf{1}}$. Calculate their wavelength, expressing your answer in meters and angstroms.

Short answer

The wavelength of the gamma rays in meter is$1.06\times {10}^{-12}m$ and in angstrom is $1.06\times {10}^{-2}{A}^0$.

Step-by-step solution

Unit of wavelength

The distance between the trough/crest, which are present at successive distances from each other, is called the wavelength and is measured in the following units of a meter, nanometer, and angstroms.

Wavelength of gamma rays.

The formula to calculate the wavelength of the radio wave is;

$Wavelenth\left(\lambda \right)=\frac{speedoflight\left(c\right)}{frequency\left(\nu \right)}$

Here,

The speed of light is $3\times {10}^{8}m{s}^{-1}$.

The frequency of the radio wave is $2.83\times {10}^{20}{s}^{-1}$.

Substituting the known value in the formula ofthe speed of the wave;

$$\begin{gathered} \lambda =\frac{3\times {10}^{8}m{s}^{-1}}{2.83\times {10}^{20}{s}^{-1}} \\ =1.06\times {10}^{-12}m \end{gathered}$$

Changing the value inangstroms;

$$\begin{gathered} 1A^0={10}^{-10}m \\ 1.06\times {10}^{-12}m=1.06\times {10}^{-2}{A}^0 \end{gathered}$$