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Dual Nature of Radiation question

2025 · 2 Apr · Shift 2 · Q60
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Dual Nature of Radiation question

2025 · 2 Apr · Shift 2 · Q60

JEE MainPhysicsDual Nature of RadiationMCQ+4 / −1
An electron with mass ' m ' with an initial velocity (t=0)v→=v0i^(v0>0)(\mathrm{t}=0) \overrightarrow{\mathrm{v}}=\mathrm{v}_0 \hat{i}\left(\mathrm{v}_0\gt 0\right)(t=0)v=v0​i^(v0​>0) enters a magnetic field B→=B0j^\overrightarrow{\mathrm{B}}=\mathrm{B}_0 \hat{j}B=B0​j^​. If the initial de-Broglie wavelength at t=0\mathrm{t}=0t=0 is λ0\lambda_0λ0​ then its value after time ' t ' would be :
  1. A
    λ01−e2 B02t2 m2\frac{\lambda_0}{\sqrt{1-\frac{\mathrm{e}^2 \mathrm{~B}_0^2 \mathrm{t}^2}{\mathrm{~m}^2}}}1− m2e2 B02​t2​​λ0​​
  2. B
    λ0\lambda_0λ0​
  3. C
    λ01+e2 B02t2 m2\lambda_0 \sqrt{1+\frac{\mathrm{e}^2 \mathrm{~B}_0^2 \mathrm{t}^2}{\mathrm{~m}^2}}λ0​1+ m2e2 B02​t2​​
  4. D
    λ01+e2 B02t2 m2\frac{\lambda_0}{\sqrt{1+\frac{\mathrm{e}^2 \mathrm{~B}_0^2 \mathrm{t}^2}{\mathrm{~m}^2}}}1+ m2e2 B02​t2​​λ0​​
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