91影视

The wavelength that is associated with an object in relation to its momentum and mass is known as the de Broglie wavelength. The de Broglie wavelength of a particle is usually inversely proportional to its strength.

Momentum of electron is,

$p=\sqrt{2m_{e}eV}$

Where, $V$is accelerating potential, $e$is the fundamental charge, $m_e$is mass of electron.

Wavelength is defined by using following formula.

$位=\frac{h}{p}$

Where, $h$ is plank鈥檚 constant and is momentum of electron.

Hence, the wavelength is,

localid="1664289974674" $\begin{array}{rcl}位& =& \frac{h}{p}\\ & =& \frac{h}{\sqrt{2m_{e}eV}}\end{array}$

In an old-fashioned television set, electrons are accelerated through a potential difference of $\text{25.0kV}$. Therefore,

$V=\text{25.0kV}$

Plank鈥檚 constant, localid="1664289980563" $h=6.626脳{10}^{鈭�34}\text{鈥塉}鈰�\text{s}$

Mass of electron, localid="1664289984939" $m_e=9.109脳{10}^{鈭�31}\text{鈥塳驳}$

Charge of electron,localid="1664289989103" $e=1.602脳{10}^{鈭�19}\text{鈥塁}$

Define the de Broglie wavelength as below.

$\begin{array}{rcl}位& =& \frac{h}{\sqrt{2m_{e}eV}}\\ & =& \frac{6.626脳{10}^{鈭�34}\text{鈥塉}鈰�\text{s}}{\sqrt{2(9.109脳{10}^{鈭�31}\text{鈥塳驳})(1.602脳{10}^{鈭�19}\text{鈥塁})(25脳{10}^3\text{鈥塚})}}\\ & =& 7.75脳{10}^{鈭�12}\text{鈥尘}\\ & =& 7.75\text{pm}\end{array}$

Hence, required de Broglie wavelength is $\begin{array}{rcl}& & 7.75\text{pm}\end{array}$.