Chapter 27, Problem 47P

To determine

The maximum possible resolution of the microscope.

Answer to Problem 47P

Solution:

The maximum possible resolution of the microscope is $2.29\times {10}^{-2}\text{nm}$.

Explanation of Solution

Given:

Voltage supplied to electrons: $2850\text{V}$

Formula Used:

$\lambda =\frac{h}{p}=\frac{h}{{\left[2m(\text{KE})\right]}^{\frac{1}{2}}}$

Calculation:

The maximum possible resolution can be determined by calculating the wavelength of the electrons.

So, by using the formula, $\lambda =\frac{h}{p}=\frac{h}{{\left[2m(\text{KE})\right]}^{\frac{1}{2}}}$

We can calculate the wavelength of the electron as

$\begin{array}{c}\lambda =\frac{h}{{\left[2m(\text{KE})\right]}^{\frac{1}{2}}}=\frac{hc}{{\left[2m{c}^2(\text{KE})\right]}^{\frac{1}{2}}}\\ =\frac{(1.24\times {10}^3\text{eV}\text{nm})}{{\left[2(0.511\times {10}^6\text{eV})(2850\text{eV})\right]}^{\frac{1}{2}}}=2.29\times {10}^{-2}\text{nm}\end{array}$

The maximum possible resolution of the microscope with a voltage supply $2850\text{V}$ is $2.29\times {10}^{-2}\text{nm}$.