An electron with mass 'm' with an initial velocity enters a magnetic field . If the initial de-Broglie wavelength at t = 0 is then its value after time 't' would be: [2025]

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Q.
An electron with mass 'm' with an initial velocity $(t = 0) \vec{v} = v_{0} \hat{i} (v_{0} > 0)$ enters a magnetic field $\vec{B} = B_{0} \hat{j}$ . If the initial de-Broglie wavelength at t = 0 is $λ_{0}$ then its value after time 't' would be: [2025]

Solution

Q.
An electron with mass 'm' with an initial velocity $(t = 0) \vec{v} = v_{0} \hat{i} (v_{0} > 0)$ enters a magnetic field $\vec{B} = B_{0} \hat{j}$ . If the initial de-Broglie wavelength at t = 0 is $λ_{0}$ then its value after time 't' would be: [2025]

1 $\frac{λ_{0}}{\sqrt{1 - \frac{e^{2} B_{0}^{2} t^{2}}{m^{2}}}}$

2 $\frac{λ_{0}}{\sqrt{1 + \frac{e^{2} B_{0}^{2} t^{2}}{m^{2}}}}$

3 $λ_{0} \sqrt{1 + \frac{e^{2} B_{0}^{2} t^{2}}{m^{2}}}$

4 $λ_{0}$

Ans.
(4)

Speed does not change due to magnetic field, that's why $λ_{debroglie}$ remains unchanged.

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Solution

Q. An electron with mass 'm' with an initial velocity (t=0)v→=v0i^(v0>0) enters a magnetic field B→=B0j^. If the initial de-Broglie wavelength at t = 0 is λ0 then its value after time 't' would be: [2025]

1 λ01–e2B02t2m2

2 λ01+e2B02t2m2

3 λ01+e2B02t2m2

4 λ0

Ans. (4) Speed does not change due to magnetic field, that's why λdebroglie remains unchanged.

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Q.
An electron with mass 'm' with an initial velocity $(t = 0) \vec{v} = v_{0} \hat{i} (v_{0} > 0)$ enters a magnetic field $\vec{B} = B_{0} \hat{j}$ . If the initial de-Broglie wavelength at t = 0 is $λ_{0}$ then its value after time 't' would be: [2025]

1 $\frac{λ_{0}}{\sqrt{1 - \frac{e^{2} B_{0}^{2} t^{2}}{m^{2}}}}$

2 $\frac{λ_{0}}{\sqrt{1 + \frac{e^{2} B_{0}^{2} t^{2}}{m^{2}}}}$

3 $λ_{0} \sqrt{1 + \frac{e^{2} B_{0}^{2} t^{2}}{m^{2}}}$

4 $λ_{0}$

Ans.
(4)

Speed does not change due to magnetic field, that's why $λ_{debroglie}$ remains unchanged.