Chapter 27, Problem 12P

To determine

Wavelength of gamma ray emission, does the wave suffer diffraction when it pass through the door?

Answer to Problem 12P

Solution:

Wavelength of gamma ray emission is $\text{0}\text{.038}\stackrel{\circ }{{\rm A}}$, and the radiation will not suffer diffraction.

Explanation of Solution

Given:

Energy of the gamma ray, $E=320\text{keV}$

Formula used:

Energy is given by the formula

$E=\frac{hc}{\lambda }$

Here,

$h=6.62\times {10}^{-34}\text{J-s}$ is Planck’s constant

$\lambda$ is the wavelength

$c=3\times {10}^8\text{m/s}$ is the speed of light

Calculation:

The wavelength of the gamma ray radiation is calculated as

$E=\frac{hc}{\lambda }$

Plugging the values in the above equation

$\begin{array}{c}320\times {10}^3\times 1.6\times {10}^{-19}=\frac{6.62\times {10}^{-34}\times 3\times {10}^8}{\lambda }\\ \lambda =0.038\times {10}^{-10}\text{m}\\ =\text{0}\text{.038}\stackrel{\circ }{{\rm A}}\end{array}$

The diffraction is a phenomenon in which wave suffers change bending when it passes through narrow slit of order of its wavelength. Since, the opening of door is of very high order than the wavelength of the radiation; therefore, wave will not suffer diffraction.: