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}

 

Answers (1)
A Aadil Khan

 

Radius of charged particle -

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

-

 

 \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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