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Dual Nature of Radiation and Matter question

2011 · Q136
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Dual Nature of Radiation and Matter question

2011 · Q136

NEETPhysicsDual Nature of Radiation and MatterMCQ+4 / −1
Electrons used in an electron microscope are accelerated by a voltage of 25 kV. If the voltage is increased to 100 kV then the de-Broglie wavelength associated with the electrons would
  1. A
    increase by 2 times
  2. B
    decrease by 2 times
  3. C
    decrease by 4 times
  4. D
    increase by 4 times
View written solutionFree

Correct answer: B

The de Broglie wavelength λ\lambda λ associated with the electrons is

λ=1.227V\lambda = {{1.227} \over {\sqrt V }}λ=V​1.227​

where V is the accelerating potential in volts.

∴\therefore∴ λ\lambda λ ∝\propto∝ 1V{1 \over {\sqrt V }}V​1​

⇒\Rightarrow⇒ λ1λ2=V2V1{{{\lambda _1}} \over {{\lambda _2}}} = \sqrt {{{{V_2}} \over {{V_1}}}} λ2​λ1​​=V1​V2​​​

= 100×10325×103\sqrt {{{100 \times {{10}^3}} \over {25 \times {{10}^3}}}} 25×103100×103​​ = 2

⇒\Rightarrow⇒ λ2=λ12{\lambda _2} = {{{\lambda _1}} \over 2}λ2​=2λ1​​

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