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An $\alpha$-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
0.01 Å
B
1 Å
C
0.1 Å
D
10 Å
Detailed Solution
Radius of the path: $r = \frac{p}{qB} = \frac{p}{2eB} \Rightarrow p = 2eBr$
$p = 2\times1.6\times10^{-19}\times0.25\times0.83\times10^{-2}$ kg m/s
$\lambda = \frac{h}{p} = \frac{6.6\times10^{-34}}{0.83\times10^{-2}\times2\times1.6\times10^{-19}\times0.25}$
$\lambda = 9.94\times10^{-13}$ m ≈ 0.01 Å
$p = 2\times1.6\times10^{-19}\times0.25\times0.83\times10^{-2}$ kg m/s
$\lambda = \frac{h}{p} = \frac{6.6\times10^{-34}}{0.83\times10^{-2}\times2\times1.6\times10^{-19}\times0.25}$
$\lambda = 9.94\times10^{-13}$ m ≈ 0.01 Å