An α-particle moves in a circular path of radius 0.83 cm in the presence of a magnetic field of 0.25 wb / m 2. The de-Broglie wavelength associated with the particle will be :-

Question

An α-particle moves in a circular path of radius 0.83 cm in the presence of a magnetic field of 0.25 wb / m 2. The de-Broglie wavelength associated with the particle will be :- (A) 1 mathringA (B) 0.1 mathringA (C) 10 mathringA (D) 0.01 mathringA

Tardigrade Admin · Accepted Answer

Using λ=( h / mv ) where mv = qBR ⇒ λ=( h / qBR ) So λ=(6.6 × 10-34/(2 × 1.6 × 10-19) ×(0.25) ×(0.83 × 10-2)) =0.01 mathringA

Q. An $α$ -particle moves in a circular path of radius $0.83 c m$ in the presence of a magnetic field of $0.25 w b / m^{2}$ . The de-Broglie wavelength associated with the particle will be :-

$1 \overset{˚}{A}$

$0.1 \overset{˚}{A}$

$10 \overset{˚}{A}$

$0.01 \overset{˚}{A}$

Using $λ = \frac{h}{m v}$
where $m v = qBR$
$\Rightarrow λ = \frac{h}{qBR}$
So
$λ = \frac{6.6 \times 1 0 ^{- 34}}{( 2 \times 1.6 \times 1 0 ^{- 19} ) \times ( 0.25 ) \times ( 0.83 \times 1 0 ^{- 2} )}$
$= 0.01 \overset{˚}{A}$

Q. An α-particle moves in a circular path of radius 0.83cm in the presence of a magnetic field of 0.25wb/m2. The de-Broglie wavelength associated with the particle will be :-

1A˚

0.1A˚

10A˚

0.01A˚