Question

An electron is accelerated through a potential difference of 10,000 V. Its de Broglie wavelength is, (nearly) :
(mₑ = 9 × 10⁻³¹ kg)
(1) 12.2 × 10⁻¹³ m
(2) 12.2 × 10⁻¹² m
(3) 12.2 × 10⁻¹⁴ m
(4) 12.2 nm

Answer 1

The de Broglie wavelength of an electron is $\bold{ 12.27\times 10^{-12}m}$.

Step by step explanation:

The de Broglie wavelength of an electron can be calculated by the following formula.

                         $\bold{\Rightarrow \frac{h}{\sqrt{2eV}}}$.......................(1)

                        h = Planks constant

                       V = Potential difference

                        e = Charge of electron.

The equation (1) can be simplified is as follows.

                        $\bold{\lambda =\frac{12.27}{\sqrt{V}}A^{o}}$..............(2)

From the given,

Potential difference = V = 10,000

Substitute the value in equation (2)

                        $\Rightarrow \frac{12.27\times 10^{-10}}{\sqrt{10000}}$

                        $\Rightarrow 12.27\times 10^{-12}m$

Therefore, The de Broglie wavelength of an electron is $\bold{ 12.27\times 10^{-12}m}$.

Hence, correct option is "2"