An electrons enters perpendicularly into uniform magnetic field having magnitude `0.5xx10^(-4)T`.If it moves on a circular path of radius 2mm,its de-Broglie wavelength is…..A

Options

A. 3410
B. 4140
C. 2070
D. 2785

Answer

B

Explanation

`B=0.5xx10^(- 4)T,r=0.2xx10^(-3)m,e=1.6xx10^(-19)C`
For electron entering perpendicular to magnetic field.
`(mv^(2))/(r )=BeV`
`therefore mv=p=Ber`
`lambda=(h)/(p)=(h)/(Ber)`
`=(6.62xx10^(-34))/(0.5xx10^(-4)xx1.6xx10^(-19)xx2xx10^(-4))`
`=(6.62xx10^(-34))/(1.6xx10^(-27))`
`=4.14xx10^(-7)` m
`therefore lambda=4140 Å`