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Question
An electron is moving with an initial velocity `v = v_0hati` and is in a magnetic field `B = B_0hatj`. Then it’s de Broglie wavelength ______.
Options
remains constant.
increases with time.
decreases with time.
increases and decreases periodically.
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Solution
An electron is moving with an initial velocity `v = v_0hati` and is in a magnetic field `B = B_0hatj`. Then it’s de Broglie wavelength remains constant.
Explanation:
If a particle is carrying a positive charge q and moving with a velocity v and enters a magnetic field 5 then it experiences a force F which is given by the expression
F = q(v × B) = $ F = qvB sin θ. As this force is perpendicular to v and B, so the magnitude of v will not change, i.e. momentum (p = mv) will remain constant in magnitude.
According to the problem, `vecv = v_0i` and `vecB = B_0j`
Magnetic force on moving electron = `-e[v_0i xx B_0j] ⇒ - ev_0B_0k`
As this force is perpendicular to `vecv` and `vecB`, so the magnitude of v will not change, i.e. momentum (p = mv) will remain constant in magnitude. Hence, de-Broglie wavelength `lambda = h/(mv)` remains constant.
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