A proton when accelerated through a potential difference of V, has a de-Broglie wavelength λ associated with it. If an α -particle is to have the same de-Broglie wavelength λ, it must be accelerated through a potential difference of

Question

A proton when accelerated through a potential difference of V, has a de-Broglie wavelength λ associated with it. If an α -particle is to have the same de-Broglie wavelength λ, it must be accelerated through a potential difference of (A) (V/8) (B) (V/4) (C) 4 V (D) 8 V

Tardigrade Admin · Accepted Answer

λp=λα (m q V)p=(m q V)α Potential difference Vα=(V/8) [ ∵ mα =4 mp qα =2 qp]

Q. A proton when accelerated through a potential difference of $V$ , has a de-Broglie wavelength $λ$ associated with it. If an $α$ -particle is to have the same de-Broglie wavelength $λ$ , it must be accelerated through a potential difference of

$\frac{V}{8}$

$\frac{V}{4}$

$4 V$

$8 V$

$λ_{p} = λ_{α}$
$(m q V)_{p} = (m q V)_{α}$
Potential difference
$V_{α} = \frac{V}{8} [∵ m_{α} = 4 m_{p} < b r / >< b r / > q_{α} = 2 q_{p}]$

Q. A proton when accelerated through a potential difference of V, has a de-Broglie wavelength λ associated with it. If an α -particle is to have the same de-Broglie wavelength λ, it must be accelerated through a potential difference of

8V​

4V​

4V

8V