Question

In an electron microscope, electron are accelerated to great velocities. Calculate the wavelength of an electron travelling with a velocity of $7.0$ megameters per second. The mass of an electron is $9.1\times {10}^{-28}g$:

• A. $1.0\times {10}^{-7}m$
• B. $9.1\times {10}^{-28}m$
• C. $1.0m$
• D. $1.0\times {10}^{-10}m$

Answer 1

Answer: (B)

$9.1\times {10}^{-28}m$

$\lambda =\frac{h}{mv}$

The concept of mass in this case should be the resistance to change in velocity of an object subjected to a certain force. According to special theory of relativity, for a given amount of force, the degree of resistance to increase in velocity of a matter increases as the original velocity approaches that of light. For the electron in this context, its velocity is quite high. So, mass at that velocity.

$mv=\frac{m_o}{(1-{\left(\frac{v}{c}\right)}^2)}{m}_o$=rest mass of electron

$=9.1\times {10}^{-31}kg$

$=9.1\times 10^{-28}g$

The correct option is B.