Question

in an electron microscope, electrons are accelerated to great velocities. calculate the wavelength of an electron traveling with a velocity of 7.0 x 10⁶ ms⁻¹. the mass of an electron is 9.1 x 10⁻²⁸ g.
○ 1.0 x 10⁻¹³ m
○ 1.0 m
○ 2.5 m
○ 1.0 x 10⁻⁷ m
○ 1.0 x 10⁻¹⁰ m

Explanation:

Step1: Recall de Broglie wavelength formula

The de Broglie wavelength formula is $\lambda = \frac{h}{mv}$, where $h = 6.626\times10^{-34}\ \text{J·s}$, $m$ is mass, and $v$ is velocity. First, convert mass to kg: $m = 9.1\times10^{-28}\ \text{g} = 9.1\times10^{-31}\ \text{kg}$.

Step2: Substitute values into formula

Substitute $h = 6.626\times10^{-34}\ \text{J·s}$, $m = 9.1\times10^{-31}\ \text{kg}$, and $v = 7.0\times10^{6}\ \text{m/s}$ into $\lambda = \frac{h}{mv}$.
$\lambda = \frac{6.626\times10^{-34}}{(9.1\times10^{-31})(7.0\times10^{6})}$

Step3: Calculate the result

First, calculate the denominator: $(9.1\times10^{-31})(7.0\times10^{6}) = 6.37\times10^{-24}$.
Then, $\lambda = \frac{6.626\times10^{-34}}{6.37\times10^{-24}} \approx 1.0\times10^{-10}\ \text{m}$.

Answer:

$1.0\times10^{-10}\ \text{m}$ (corresponding to the option "1.0 x 10⁻¹⁰ m")