Question

An $\alpha$ particle moves in circular orbit a of radius $1.4cm$ in a magnetic field of $6.6T$. Find the deBroglie wavelength associated with the particle.

• A. $2.2\times {10}^{-14}\text{m}$
• B. $4.2\times {10}^{-14}\text{m}$
• C. $6.6\times {10}^{-14}\text{m}$
• D. $1.4\times {10}^{-14}\text{m}$

Answer 1

The correct option is A $2.2\times {10}^{-14}\text{m}$

$r=\frac{mv}{qB}$
$mv=qBr$
$\lambda =\frac{h}{p}=\frac{h}{mv}=\frac{h}{qBr}$
$=\frac{\text{/}6.6\times {10}^{-34}}{2\times 1.6\times {10}^{-19}\times \text{/}6.6\times 1.4\times {10}^{-2}}$
$=\frac{{10}^{-15}\times {10}^2}{2\times 1.6\times 1.4}=\frac{{10}^{-13}}{2\times 1.6\times 1.4}$
$=2.2\times {10}^{-14}\text{m}$