An electron, accelerated by a potential difference V, has de-Broglie wavelength λ . If the electron is accelerated by a potential difference 4V, its de-Broglie wavelength will be

Question

An electron, accelerated by a potential difference V, has de-Broglie wavelength λ . If the electron is accelerated by a potential difference 4V, its de-Broglie wavelength will be (A) 2 λ  (B) 4 λ  (C)  ( λ / 2)  (D)  ( λ / 4)

Tardigrade Admin · Accepted Answer

From the relation, λ = ( h / √ 2 m e V ) ..(i) So, when V becomes 4V, then λ ' = ( h / √ 2 m e (4 V) ) ⇒ λ ' = ( h / 2 √ 2 m e V ) ⇒ λ ' = ( λ / 2)

Q. An electron, accelerated by a potential difference V, has de-Broglie wavelength $λ$ . If the electron is accelerated by a potential difference 4V, its de-Broglie wavelength will be

2 $λ$

4 $λ$

$\frac{λ}{2}$

$\frac{λ}{4}$

From the relation,
$λ = \frac{h}{2 m e V}$ ..(i)
So, when V becomes 4V, then
$λ^{'} = \frac{h}{2 m e ( 4 V )}$
$\Rightarrow λ^{'} = \frac{h}{2 2 m e V}$
$\Rightarrow λ^{'} = \frac{λ}{2}$

Q. An electron, accelerated by a potential difference V, has de-Broglie wavelength λ. If the electron is accelerated by a potential difference 4V, its de-Broglie wavelength will be

2 λ

4λ

2λ​

4λ​