# An $\alpha$-particle moves in a circular path of radius 0.83cm in the presence of a magnetic field of  $0.25 \ Wb/m^{2}$. The wavelength associated with the particle will be: Option 1) 1$\overset {o}{A}$ Option 2) 0.1$\overset {o}{A}$ Option 3) 10$\overset {o}{A}$ Option 4) 0.01$\overset {o}{A}$

$r=\frac{mv}{qB}=\frac{P}{qB}=\frac{\sqrt{}2mk}{qB}=\frac{1}{B}\sqrt{}\frac{2mV}{q}$

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$\gamma =\frac{p}{qB}=p=qB\gamma \rightarrow 1\\ \therefore \:wavelength\:\lambda =\frac{h}{p}=\frac{h}{qBr}\\ h=6.62\times 10^{-34}$

$q=2\times 1.6\times 10^{-19c},B=0.25,\gamma =0.83cm\\ \therefore \:\lambda =0.01A^o$

Option 1)

1$\overset {o}{A}$

This solution is incorrect

Option 2)

0.1$\overset {o}{A}$

This solution is incorrect

Option 3)

10$\overset {o}{A}$

This solution is incorrect

Option 4)

0.01$\overset {o}{A}$

This solution is correct

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